Planck Stars the final fate of quantum no-singula black hoes and its phenoenoogical cosequences
Francesca Vidotto UPV/EHU - Bilbao
SINGULARITIES OF GENERAL RELATIVITY AND THEIR QUANTUM FATE Warsaw - May 23rd, 2018 Planck Stars the final fate of quantum no-singula black hoes and its phenoenoogical cosequences
Francesca Vidotto UPV/EHU - Bilbao
SINGULARITIES OF GENERAL RELATIVITY AND THEIR QUANTUM FATE Warsaw - May 23rd, 2018 QUANTAQUANTA OF OFSPACE SPACETIME
It is a theory about quanta of spacetime Each quantum is Lorentz invariant
The states are boundary states at fixed time SL(2, C) SU(2) ! i The physical phase space is spanned by SU(2) group variables L⌅ = L ,i=1, 2, 3 l { l} gravitational field operator (tetrad) SU(2) generators
i i Geometry is quantized: A = LlLl. l ⇥ 2 2 i j k VR = Vn,Vn = ijkLlL Ll” . 9 | l | n R Discrete spectra: minimal non-zero eigenvalue
Spinfoam & Singularities Francesca Vidotto QUANTIZATION OF THE CLASSICAL ACTION
1 GR action S[e, !]= e e F ⇤[!]+ e e F [!] (Holst term) ^ ^ ^ ^ Z Z BF theory S[e, ]= B[e] F [ ] ^ Z 1 Canonical variables ⇥,B=(e e)⇤ + (e e) ^ ^
a i On the boundary n = e n nie =0 SL(2, C) SU(2) i i a ! ni =(1, 0, 0, 0) B (K = nB, L = nB⇤) !
Simplicity constraint
K
Spinfoam & Singularities Francesca Vidotto QUANTIZATION OF THE CLASSICAL ACTION
1 GR action S[e, !]= e e F ⇤[!]+ e e F [!] (Holst term) ^ ^ ^ ^ Z Z BF theory S[e, ]= B[e] F [ ] ^ Z 1 Canonical variables ⇥,B=(e e)⇤ + (e e) ^ ^
a i On the boundary n = e n nie =0 SL(2, C) SU(2) i i a ! ni =(1, 0, 0, 0) B (K = nB, L = nB⇤) !
Boost generator Rotation generator Rovelli,Vidotto 1307.3228
Maximal acceleration: no curvature singularities! (spacetime can be geodesically incomplete for some artificially patched manifolds Geroch ‘68)
Spinfoam & Singularities Francesca Vidotto BH EXPLOSION
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Quantum Black Holes Francesca Vidotto BH EXPLOSION
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Quantum Black Holes Francesca Vidotto Scenario 1
Quantum Black Holes Francesca Vidotto
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in
solution
search
of
the
in
dilaton
an
expansion
to
ds
of
It depends only on the original mass Mo at the BH formation to
an
expansion to
solution
search
room
solution
dilaton
search
procedure
ds
snapshot
to
The
to
room
snapshot
procedure
dilaton
ds
The
dilaton object
to snapshot
T ds as
room procedure
⇠ ⇠ current densitysnapshot ⇢ of remnants is of the order room
of
procedure The object
The to as
Of
of
object
the
object
Of
the
as is
to of fairly
as a
to
behaved the of
Of the
H the
Of is
fairly
behaved a
the
the the
the
the
fairly
on Earth isbehaved due to the strong source of negative en-
is
Christodoulou, De Lorenzo1604.07222 fairly
a behaved is
a
the
the
come
geometry
itational attraction. Therefore the original negative en- come
of geometry
time tropy driving irreversibility around us can be traced to
of geometry time
geometry
come
come
time
time
of of
time.
first-order
=
attempt
time.
line first-order
manifold
first-order
time.
= first-order
line
time. attempt
manifold
=
line the
attempt
line the
=
the the manifold
attempt the
manifold
inconsistent the
for
the
for
the for inconsistent
~~oo. inconsistent for
that
~~oo.
~~oo.
that
inconsistent
that
that
~~oo.
At
At At At
course,
course, course,
If we take the mass of each remnant to becourse, Planckian
solutions
solutions
solutions
solutions
solution
other
expansion that
explicitly
solution
other
solution
expansion
other
that explicitly that
that solution
other expansion
explicitly
expansion
—
an
explicitly
— an
— —
metric
an
for
for
metric
an
metric
Oat
for for
metric
for
for
for Oat
Oat
for Oat but
ergy formed by the sun; the sun in turn was irreversiblyin symmetric
field but
in
the
arbitrary any
in
field symmetric
but
in
the
symmetric any
arbitrary dilaton,
of
dH+a(r)
as
but
symmetric
field dependence
by the
the early lackarbitrary of gravitational clumping. As repeatedly any dilaton,
of
as
dH+a(r)
the
dependence
field arbitrary
undetermined. by
dilaton, dynamics
tropy driving irreversibility around us can be traced to of dH+a(r)
any
as by
dilaton, of
dH+a(r)
of dependence
undetermined.
dynamics
by
we of
as
undetermined. dynamics
dependence
up
dynamics
we
undetermined.
everywhere
of around
1 up
we
a everywhere
around
up
of patching
[15], namely of order unit in Planck units, ⇢ is also their Our
we
a
up
a
everywhere
around
patching
the Our
If we take the mass of each remnant to be Planckian form
a
a
for
everywhere
around
patching
a
Our the
form
perturbatively,
a a
for
smooth a
patching
assuming motion
a
Our
the
sensible
form a
perturbatively, a
coefficient
smooth
for
we
motion assuming
finite
the
form sensible
this
a
coefficient
perturbatively,
equations
smooth
a
we
for
assuming
have finite
motion
finite collapsing
this
sensible
We
equations
a with
smooth
coefficient
perturbatively,
assuming
have
shown a
collapsing
motion we
⇢ ⇢ . (6) formed by the collapse of a primordial cloud under grav- finite finite
with
this
We
sensible
with
M finite
coefficient
shown
equations
pointed out by Penrose,to the fact that the geometry of functions
finite
have
we
finite with collapsing
this
finite
with
We
to
functions
the early lack of gravitational clumping. As repeatedly finite equations
collapsing
2 shown
all
have
so
with
ordinary collapsing
with
We
finite
to
functions matching of collapsing
all
shown
so with
number density in the units we are using. From the big ordinary
feel
to
matching of
functions
finite
the
collapsing
all
so
is
in demonstration of
[15], namely of order unit in Planck units, ⇢ is also their ordinary T feel
⇠ ⇠ with
the
matching of
collapsing
assumption
is
all
in demonstration
the
can so
of
ordinary
with
time
H feel
of matching
finite
the
described,
obtained
assumption keep
the
can
is
in
of demonstration
the
a
time
the
with
region.
finite
inconsistent.
described,
feel
obtained
keep
itational attraction. Therefore the original negative(dr en-
the
the universe wasassumption small and homogenous to the degree re-
of
powers
is
the
the
gives can
of
in
solutions the
a
in
demonstration
the
region.
with
inconsistent.
volume
time
ansatz
(dr
finite
keep
obtained
described,
of
powers
solutions assumption
gives
pointed out by Penrose, the fact that the geometry of in
in
solutions the existence occurs
the
can the
confident
a
natural
volume the
region. ansatz
inconsistent.
shell,
bounce to the current epoch the universetime has widely ex-
keep (dr
finite
solutions
obtained
in
described, a
occurs existence
of
powers
confident
gives
4 solutions
the in
the
natural the
smooth
then
the a
the
a
region.
shell,
cornucopion.
volume inconsistent.
ansatz
that
topology
number density in the units we are using. From the big (dr
a
functions,
vacuum
solutions
after
see Bianchi’s talk of
gives
the
in powers
smooth existence
solutions
occurs then
the the in
confident
a cornucopion. Fig.
REMNANT LIFETIME ~ Mo natural cosmological +r
metric,
that
topology
shell, values
functions, volume
ansatz
vacuum
nonsingular
after
and
a
solutions
Fig.
Thus
existence in the
occurs quired by the current standard cosmological model, im-
the cosmological
+r
smooth
then
confident
natural
tropy drivingdifferential irreversibility around us can be traced to
metric,
the
a
values
cornucopion.
nonsingular
shell,
shell,
and
topology
that
conditions functions,
vacuum
a
collapsing
rise
after
Thus
field
differential
the the the
the universe was small and homogenousFig. to the degree re-
then smooth
cosmological +r
a shell,
panded. Assuming at least 60 e-folding, the bounce is metric,
to
that values
cornucopion.
does
If we take the mass of each remnant to be Planckian conditions
nonsingular topology
collapsing
rise
and
that is
of
vacuum
field functions,
We
use
dQ
after
Thus
behaves
only
differential
the
cosmological +r
Fig. to
2. that
its
does
cornu- metric,
bounce to the current epoch the universe has widely ex- shell,
is
values of
begins
We
nonsingular
conditions
dilaton
and use
dQ
rise collapsing
ansatz. that
behaves
only
field
static
Thus
verify
2.
its
cornu-
of
the
differential
n plies a very ‘special’ state determining an initial low en-
(2. begins
three- to
that shell, solu- dilaton
the earlydoes lack of gravitational clumping. As repeatedly to
there
ansatz. that
of
Time needed for information to leak out from such a large volume trough the small WH surface. conditions
equa-
of
of exist.
is We
rise
static
collapsing that
leav- dQ
use field
verify
for-
behaves
only of
will
of
We
with
n
have
field
this
(2.
not
three-
solu- ) 2.
not very far from the epoch whereits the horizon is Planck- of
cornu-
are
to
quired by the current standard cosmological model, im- there
of
to
equa- of
exist.
that
does
begins
that
[15], namely of order unit in Planck units, ⇢ is also their dilaton
We
leav-
in
13)
We
ansatz. for-
that of
is
will dQ
of We
FIG. 2. the
use
with
static
The interior geometry of an old black hole: a very to
have
field this
behaves
in-
not verify
~.
only
)
of
of
are
a
an
a
n
(2. 47
three-
2.
its
panded. Assuming at least 60 e-folding, the bounce is cornu-
solu- We
in
13)
to
there
a
equa-
of
exist.
begins dilaton
of
the
ansatz. that
to
leav-
that
in-
~.
for- tropy.
will
a
of static
We
with
an a have
verify
field
of
this
47 not
pointed out by Penrose, the fact that the geometry of ) of
n
are
three-
a (2.
solu-
to
We
there
equa-
13) in
exist. long thin tube, whose length increases and whose radius de- of
ian, which gives a linear expansion factor of the order of of
leav-
the
that
to
in-
for-
plies a very ‘special’ state determining an initial low en-~.
will with
of
number density in the units we are using. From the big have
We
field
a
an
this
)
a
not 47
of
are
a
We 13)
in FIG. 3. The transition across the
not very far from the epoch where the horizon is Planck- the to
A region. in-
~.
an
a creases with time. Notice it is finite, unlikely the Einstein- 47 the universe wasa smallBut and if homogenous the remnant to scenario the degree is correct, re- the geometry at bounce to the currenttropy. epochTH and the therefore universe a has volume widely expansion ex- factor of the order a ian, which gives a linear expansion factor of theRosen order bridge. of 3 quired by the currentthe standard bounce had cosmological far more volume model, and im- was not homogenous panded. Assuming at leastof TH 60.Tohavethesu e-folding, the bouncecient density is of remnants today TH and therefore a volume expansion factor of the order But if the remnant scenario is correct, the geometryµ⌫⇢ at at all. To the opposite, it was very highly crumpled. If BOUNCING BLACK HOLES IN A BOUNCINGto saturateUNIVERSE dark matter, we needinvariant a densitypliesK of aR veryµthe⌫⇢ R order ‘special’is easily state computed determining to be an initial low en- of T 3 .Tohavethesu cient density of remnantsnot very far today from thethe epoch bounce where had the far horizon more volume is Planck- and was not⌘ homogenous so, what is the2 origin of past low entropy, if it is not how H tropy. 2 2 4 ian, whichthe two gives regions aA linearand B expansionwhere classical factor general of relativity the order3 of 9 l 24 l⌧ + 48 ⌧ to saturate darkPlanckian matter, wePBH need remands a density from of a theprevious order eon (Penrose’sat all. To EREBONS the opposite,) ⇢ it was⇢T veryT highlyK crumpled.(⌧) (7) If specialm the2 initial geometry was? becomes unreliable. b H H But if the remnant2 8 scenario is correct,(5) the geometry at TH and therefore a volumeso, what expansion is the origin factor of of past⇠ the low order⇠ entropy, if it is⇡ not how(l + ⌧ ) Planck ofsize the particles matter can density pass⇢ troughM 3, andRegion the this bounce.A inis characterised turn is related by large to curvatureof and gravity, covers Quintin, to which Brandenberger genericthe bounce evolution 1609.02556 had far tends, more are volume highly and was not homogenous 3 of TH .Tohavethesuthe singularity. According atcient to the classical density bounce. general of Using relativity remnants (4) we today haveCarr,in the anClifton, large amount massColey limit, of1704.02919 internal which has the finite maximum ⇢bTH by⇢T4H the FriedmannTH equation (7) special the initialcrumpled, geometry notwas? homogeneous. (For interesting criticisms We want⇠ Mo ≥ ⇠tHubble for themto saturate tothe survive singularity dark till nevermatter, today. reachesvolume we the need horizon. per a unit density (N.B.: of Two external of the order volume at all. To the opposite, it was very highly crumpled. If and informed alternative perspectives, see9 m [382 –41].) lines2 meeting at the boundary of a conformal diagram so, what isK the(0) origin. of past lowIV. entropy, PERSPECTIVAL if it is not how ENTROPY at the bounce. Using (4) we have an amount of internal 6 (6) 1 adoes˙ not mean that they meet in3 the physical spacetime.)The fact that source2 of past low entropy,⇡ l hence the Inflation dilutes PBH: ⇢M , ⇢b ⇢TH (5)TH Vint = ⇢bVWH(7)>TH .special the initial(8) geometry was? volume per unit of external volume T 2 ⇠ a Region⇠ B, instead, surrounds⇠ the⇠ end of thesource evapora- of irreversibility, was the homogeneity of space H ✓ ◆ IV. PERSPECTIVALFor ENTROPY all the values of ⌧ where l An⌧ 2 imposing< 2m the line aspects of the Cosmos is the mighty daily tion, which involves the horizon, and a ↵isects confirmed what hap- by a simple analysis of the thermodynam-⌧ 2 at the bounce. Using (4This) we means have an that amount only a of fraction internalelement is well approximated by takingrotationl = 0 which of Sun, gives Moon, planets, stars and all galaxies Vintwhere= ⇢bVWH we neglect>TH . factors ofpens order outside(8) unit. the hole. Therefore Taking evaporation the intoical account, history of the universe. For instance irreversibility volumethe per area of unit the horizon of external shrinks progressively volume until reach- 4 2 2 120 2 4⌧ 2 2m ⌧around2 us.4 Why does the Cosmos rotate so? Well, it is PAST currentLOW ENTROPY density ⇢ of remnants is of the orderAn imposing aspectson Earth1 of/T theH is Cosmos10 due tods theis= the strong mightyIV. sourced⌧ daily+(9) PERSPECTIVAL of negativedx + ⌧ d en-⌦2. ENTROPY(7) ing region B. ⇠ 2m ⌧ 2 ⌧ 2 not the Cosmos rotating, it is us. The rotation of the sky This means that only a fraction 2 ergy formed by the sun; the sun in turn was irreversibly Matter near thermal equilibrium: geometryThe quantum1 hasV gravitationalintrotation low= ⇢entropybV eWH of↵ects Sun,>T inH regions. Moon,A and planets,B (8) stars and all galaxies is a perspectival phenomenon: we understand it better as ⇢ ⇢ are distinct,. and confusingof them the is volume a source(6) of of misun-formed the universe by the was collapseFor outside⌧ < of0, the this a primordial remnants is the Schwarzschild at cloud metric under inside grav- the 2 120 M 2 around us. Why does the Cosmosblack rotate hole, asAn canso? imposingbe readilyWell, seen it aspects is goingdue to Schwarzschild of to the the Cosmos peculiarity is the of mighty our own daily moving point of view, Only 1 /T H 10 of the ⇠volumederstanding.⇠ ofTH (9)the Notice universe thatthe a generic was bounce. outside spacetime If the we region assumeremnants in equiprobability at the bounce! for each equal ⇠ This means that onlynot a the fraction Cosmos rotating,itational it attraction. is us.coordinates The Therefore rotation of the the original sky negative en- A is spacelike separatedvolumeand in general of the universe, the probabilityrotation for an observer of Sun, to Moon,rather planets, than as stars a global and feature all galaxies of all celestial objects. is a perspectival phenomenon:verytropy distant drivingfrom we irreversibility understand around it better us as can be traced to of the volume of the universeIf we take was the outside mass the of remnants eachregion remnantB. By at locality, to be therebe2 Planckian is outside no reason120 to those expect remnants these at the bouncearound is one us. part Why in doesThe the2 list Cosmos of conspicuous rotate so? phenomena Well, it that is have turned out 1/T 10 (9) ts = x, and rs = ⌧ . (8) [15], namely of order unit intwo Planck regions to units, influencedue⇢ oneisH to also another.120 the their peculiaritythe early of our lack own of gravitational moving point clumping. of view, Asto repeatedly be perspectival is long; recognising them has been a the bounce. IfPlanck we assume Stars equiprobability for each equal 10 ⇠. Therefore an observer outside thenotFrancesca remnants the Cosmos Vidotto is in rotating, it is us. The rotation of the sky number density in the unitsThe we quantum are using. gravitationalrather From than the physical big as process apointed global happening feature out byFor Penrose, of⌧ all120> 0, celestial this the is the fact Schwarzschild objects. that the metricpersistent geometry inside a aspect of white of the progress of science. volume of the universe, the probability forof an the observerat volume these two to of regions the must universe bethis considered sense was outside ‘special’ separately. the as remnantsone part in at 10 is. a perspectival phenomenon: we understand it better as bounce to the current epoch the universeThe has widely list of conspicuous ex- the universe phenomena washole. small that Thus and the have metric homogenous turned ( 4) represents out to the a continuousThe degree hypothesis re- transi- put forward in [26] is that the increase be outside those remnants at the bouncethe is one bounce. part If in we assume equiprobabilityquired for by each the equal currenttion of the standarddue geometry to the of cosmological a black peculiarity hole into the model, of geometry our ownim- of moving point of view, 120 panded. Assuming at least 60 e-folding,to the be bounce perspectival is is long; recognising them has been a of entropy is a perspectival phenomenon in this sense. To 10 . Therefore an observer outside thevolume remnants of the is in universe, the probabilityplies for an a veryobserver ‘special’a to white state hole,rather across determining thana region as of Planckian, a an global initial but feature bounded low en- of all celestial objects. not very far from the epoch where the horizon is Planck- III. PAST LOWcurvature. ENTROPY be sure, it is not subjective or mental, or illusory. Rather, this sense ‘special’ as one part in 10120. be outsideIII. those THE remnantsApersistentREGION: at TRANSITIONING the aspect bounce of the is progressone part of in science.The list of conspicuous phenomena that have turned out ian, which gives a linear expansion factor of the order of tropy. Geometrically, ⌧ = constant (space-like)its source surfaces is in foli- the relation between an observer system 120 ACROSS THEThe SINGULARITY hypothesis put forward in [26] isto that be the perspectival increase is long; recognising them has been a 10 . Therefore an observer outside theBut remnants if the remnant isate in the interior scenario of a black is correct, hole. Each the of theseand geometry surfaces an observed at system, like for the rotation of the sky. TH and therefore a volume expansion factor of theThe order mystery120 of the second principle of thermodynam-2 3 this sense ‘special’ asof one entropy part is in a 10 perspectivalthe. bounce phenomenon had farhas the more topologypersistent in volume this sense. and aspectR was, namely To not of is the a homogenous long progress cylinder. As of science. of TH .Tohavethesu cientTo density study the ofA remnantsregion,ics let is us todaynot focus why on an entropy arbitrary growth towards the future.S ⇥ That’s This is possible because the entropy of a system de- III. PAST LOW ENTROPY be sure, it is not subjectiveat all. To or the mental, opposite,time passes, or illusory. itThe the was radial hypothesis very size Rather, of highly the cylinder put crumpled. forward shrinks while in If [26] is that the increase to saturate dark matter, wefinite need portion a density of the collapsing ofpretty the interior order obvious. tube. As we The ap- mystery isthe why axis entropy of the cylinder diminishes gets stretched. Aroundpends on the system’s microstate but also on the coarse proach the singularity,its the source Schwarzschild is in radiusthe relation between anof observer entropy is system a perspectival phenomenon⌧ =0 in this sense. To going towards theso, what pastrs,which [ is30 the–35]. originthe All cylinder current of past reaches lowirreversible a minimal entropy, size, ifandgraining it then is not smoothly how under which the system interacts. The relevant is a3 temporalIII. coordinate PASTand inside an LOW the observed hole, ENTROPY decreases system, and like for the rotationbe sure, of it the is not sky. subjective or mental, or illusory. Rather, The mystery of the second principle of⇢ thermodynam-b ⇢TH TH phenomena,(7) includingspecial our the own initialbounces future-oriented geometry back and was? starts thinking, increasing its radialcoarse size graining and is determined by the concrete existing ⇠ the curvature⇠ increases. When the curvature approaches shrinkingits its length. source The is cylinder in the never relation reaches zero between size an observer system ics is not why entropy growth towards the future.Planckian That’s values, the classicalThisthe approximation existenceis possible of becomes because memories the and entropy the direction of a system of causal- de- interactions with the system. The entropy we assign to at the bounce. Using (4) we have an amount of internal but bounces at a small finite radius l. The Ricci tensor pretty obvious. The mystery is why entropyThe diminishesunreliable. mystery Quantum of thepends gravity secondity on e we principle the use↵ects system’sto are make expected of thermodynam- sense microstate to of the world,but alsoand canon an be theobserved traced coarse to system,systems like around for the us rotation depends of on the the sky. way we interact with volume per unit of external volume vanishes up to terms O(l/m). going towards the past [30–35]. All currentics is irreversiblebound not why the curvature entropygraining [ growth7–the10, 12 fact under– towards18 that, 21–23 which entropy, the26, 28 future. the, was59, system60 low]. That’s in interacts. theThe resulting pastThis [36 The geometry, 37 is]. relevant possible Since is depicted because inthem Figure – asthe the entropy apparent of motion a system of the de- sky depends on our Let us see what a bound on the curvature can yield. Fol- IV. PERSPECTIVAL ENTROPY 3.The phenomena, including our own future-orientedpretty thinking, obvious.2 Thecoarse mysterymatter graining is was why apparently is entropy determined diminishes near thermal byregion the around equilibriumpends concrete⌧ = on 0 is the the existing in smoothing the system’s ofown the microstate central motion. blackbut also on the coarse Vint = ⇢blowingVWH [>T61], consider. the line element(8) going towardsH the pastpast, [30–35 the]. low All entropy current was irreversible concentratedhole singularitygraining on the at geometry.r unders = 0. which theThis system observation interacts. opens The a novel relevant way for facing the puz- the existence of memories and the direction of causal- interactions with the system. TheThis entropy geometry we can be assign given a simple to physical interpre- 4(⌧ 2 2 In fact,2 in standardAn cosmology imposing aspects geometrycoarse of the is assumed Cosmos graining tois is the determinedzle mighty of the daily arrow by the of concrete time: the existing universe is in a generic This means that onlyphenomena, a fraction2 including+ l)systems our2 2m own around⌧ future-oriented2 us2 depends2 thinking, on thetation. way Generalwe relativityinteract is not with reliable at high curva- ity we use to make sense of the world, can be tracedds = to d⌧ + dx +(⌧rotation+l) d⌦2, of(4) Sun, Moon, planets, stars and all galaxies the existence 2 ofm memories⌧ 2 be⌧ nearly2 and+ l the homogenous. direction of For causal- theture, gravitational becauseinteractions of quantum field, gravity. with ho- Therefore thestate, system. the but “pre- The su ciently entropy rich we to assign include to subsystems whose the fact that entropy was low in the past [36, 37]. Since them – as the apparent motion of the sky depends on our 2 120 mogeneity is aaround very low us. entropy Whydiction” does configuration, ofsystems the the singularity Cosmos around because by rotate the us classical so? dependscoupling theory Well, hason it defines no theis way a coarsewe interact graining with for which entropy in- matter was apparently near thermal equilibrium1ity/TH we use10 in to the makeown sense motion. of the(9) world, can be traced to where⇠ l m. This line elementgravity defines tends a genuine tonot clump Rieman- the Cosmos and genericallyground. rotating, High the it curvature is evolution us. Theinduces ofrotation quantumcreases of particle the monotonically. skycre- These subsystems are those where the factnian thatspacetime,⌧ entropy with no was divergences low in and the no singularities. past [36, 37]. Since them – as the apparent motion of the sky depends on our past, the low entropy was concentrated on the geometry. This observationis opens a perspectival a novelation,phenomenon: way including for facing gravitons, we the understand and puz- these can it have better an e as ↵ec- of the volume of the universematterCurvature was was outside apparently is bounded. the For remnantsperturbations near instance, thermal the at Kretschmann leads equilibrium increasingly in the awayown from motion. homogene- information can pile up and ‘information gathering crea- In fact, in standard cosmology geometry is assumed to zle of the arrowdue of time: to the the peculiarity universetive energy of momentum is our in own a tensor generic moving that back-reacts point of on view, the the bounce. If we assumepast, equiprobability the low entropy for wasity. each concentrated In equal fact, as longon the argued geometry. by Penrose,This generic observation states openstures’ a such novel as way those for composing facing the the puz- biosphere can exist. be nearly homogenous.volume For of the the gravitational universe, the field,probability ho- forstate, an observer but su to cientlyrather rich than to as include a global subsystems feature of whose all celestial objects. mogeneity is a very low entropy configuration,In fact, because in standardcoupling cosmology defines geometry aThe coarse is list assumed of graining conspicuous to for whichzle phenomena of entropy the arrow that in- have of time: turned the out universe is in a generic be outside those remnantsbe nearly at the homogenous. bounce is one For part the in gravitational field, ho- state, but su ciently rich to include subsystems whose gravity tends to clump120 and generically the evolution of creases monotonically.to be These perspectival subsystems is long; are recognising those where them has been a 10 . Therefore an observermogeneity outside is a very the remnants low entropy is in configuration, because coupling defines a coarse graining for which entropy in- perturbations leads increasinglythis sense ‘special’ away as from one homogene- part in 10120. information can pilepersistent up and aspect ‘information of the progress gathering of science. crea- gravity tends to clump and generically the evolution of creases monotonically. These subsystems are those where ity. In fact, as long argued by Penrose, generic states tures’ such as thoseThe composing hypothesis the put biosphere forward can in [26 exist.] is that the increase perturbations leads increasingly awayof from entropy homogene- is a perspectivalinformation phenomenon can pile in this up sense. and ‘information To gathering crea- III. PASTity. LOW In fact, ENTROPY as long argued by Penrose,be sure, generic it is notstates subjectivetures’ or such mental, as thoseor illusory. composing Rather, the biosphere can exist. its source is in the relation between an observer system The mystery of the second principle of thermodynam- and an observed system, like for the rotation of the sky. ics is not why entropy growth towards the future. That’s This is possible because the entropy of a system de- pretty obvious. The mystery is why entropy diminishes pends on the system’s microstate but also on the coarse going towards the past [30–35]. All current irreversible graining under which the system interacts. The relevant phenomena, including our own future-oriented thinking, coarse graining is determined by the concrete existing the existence of memories and the direction of causal- interactions with the system. The entropy we assign to ity we use to make sense of the world, can be traced to systems around us depends on the way we interact with the fact that entropy was low in the past [36, 37]. Since them – as the apparent motion of the sky depends on our matter was apparently near thermal equilibrium in the own motion. past, the low entropy was concentrated on the geometry. This observation opens a novel way for facing the puz- In fact, in standard cosmology geometry is assumed to zle of the arrow of time: the universe is in a generic be nearly homogenous. For the gravitational field, ho- state, but su ciently rich to include subsystems whose mogeneity is a very low entropy configuration, because coupling defines a coarse graining for which entropy in- gravity tends to clump and generically the evolution of creases monotonically. These subsystems are those where perturbations leads increasingly away from homogene- information can pile up and ‘information gathering crea- ity. In fact, as long argued by Penrose, generic states tures’ such as those composing the biosphere can exist. 2 2 of the matter density ⇢M , and this in turn is related to of gravity,of the matter to which density generic⇢M , and evolution this in tends, turn is arerelated highly to of gravity, to which generic evolution tends, are highly TH by the Friedmann equation crumpled,TH by the not Friedmann homogeneous. equation (For interesting criticisms crumpled, not homogeneous. (For interesting2 criticisms and informed alternative perspectives, see [38–41].) and informed alternative perspectives, see [38–41].) 2 1 a˙ 2 1 a˙ of the matter density ⇢M , and this in turn is related to of gravity, to which genericThe fact evolution that source tends, of are past highly low entropy, hence the The fact that source2 of past low⇢M entropy,, hence(5) the 2 ⇢M , (5) T ⇠ a ⇠ source of irreversibility, was the homogeneity of space WHITET ⇠ HOLESa ⇠ AS REMNANTSTH by the Friedmann 1source equation of irreversibility,H was✓ ◆ the homogeneitycrumpled, of not space homogeneous. (For interesting criticisms H ✓ ◆ Bianchi, Cristodoulou, D’Ambrosio, Haggard, Rovelli 1802.04264 is confirmed by a simple analysis of the thermodynam- is confirmed by a simple analysis of theand thermodynam- informed alternative perspectives, see [38–41].) where2 we neglect factors of order unit. Therefore the ical history of the universe. For instance irreversibility where we neglect factors of order unit. Therefore the 1 a˙ The fact that source of past low entropy, hence the icalcurrent history density of⇢ the, ⇢ universe.of remnants For is(5) of instance the order irreversibility on Earth is due to the strong source of negative en- current density ⇢ of remnants is of the order 2 M TonH ⇠ Eartha is⇠ due to the strong sourcesource of negative of irreversibility, en- ergy was formed the by homogeneity the sun; the sun of space in turn was irreversibly ✓ ◆ Christodoulou,1 Rovelli 1411.2854 LARGE INTERNAL VOLUME ~ Mo4 ergy formed by the sun;⇢ the⇢ sun in. turnis was confirmed irreversibly by(6) a simpleformed analysis by the collapse of the thermodynam- of a primordial cloud under grav- 1 where we neglect factors of order unit. ThereforeMBengtsson, theT 2 Jakobsson 1502.01907 ⇢ ⇢M . (6) formed by the collapse of⇠ a primordial⇠ H cloudical history under of grav- the universe. For instance irreversibility It depends only on 2the original mass Mo at the BH formation Ong 1503.08245 itational attraction. Therefore the original negative en- ⇠ ⇠ TH current density ⇢ of remnants is of the order Christodoulou, Deon Lorenzo1604.07222 Earth is due to the strong source of negative en- itationalIf we attraction. take the mass Therefore of each remnant the original to be negative Planckian en- tropy driving irreversibility around us can be traced to ergy formed by the sun; the sun in turn was irreversibly If we take the mass of each remnant to be Planckian tropy[15 driving], namely1 irreversibility of order unit in around Planck us units, can⇢ beis also traced their to the early lack of gravitational clumping. As repeatedly ⇢ ⇢ . (6) formed by the collapse of a primordial cloud under grav- thenumber earlyM lack density2 of gravitational in the units we clumping. are using. As From repeatedly the big pointed out by Penrose, the fact that the geometry of [15], namely of order unit in Planck units, ⇢ is also their ⇠ ⇠ TH pointedbounce out to by the Penrose, current epoch the fact the universe thatitational the has geometry widely attraction. ex- of the Therefore universe the was original small and negative homogenous en- to the degree re- number densityREMNANT in the units LIFETIME we are using. ~ FromMo4 see the Bianchi’s big talk tropy driving irreversibilityquired by around the current us can standard be traced cosmological to model, im- bounce to the current epoch the universeIf has we widely take the ex- massthe ofpanded. universe each remnant Assumingwas small to beat and least Planckian homogenous 60 e-folding, to the the bounce degree isre- Time needed for information[15 to], namelyleak out of from order suchquired unitnot a inlarge by very Planck the volume far current from units, trough the⇢ standard epochis alsothe wheresmall their cosmological theWH horizonthe surface. early model, is Planck- lack im- of gravitationalplies a very clumping. ‘special’ state As determiningrepeatedly an initial low en- panded. Assuming at least 60 e-folding, the bounce is tropy. number density in theplies unitsian, a very which we are ‘special’ gives using. a linear state From expansion determining the big factorpointed an of initial the out order low by en-of Penrose, the fact that the geometry of not very far from the epoch where the horizon is Planck- But if the remnant scenario is correct, the geometry at bounce to the currenttropy. epochTH and the therefore universe a has volume widely expansion ex- factorthe universe of the order was small and homogenous to the degree re- ian, which gives a linear expansion factor of the order of of T 3 .Tohavethesu cient density ofquired remnants by the today currentthe standard bounce had cosmological far more volume model, and im- was not homogenous panded. Assuming atBut least ifH the60 e-folding, remnant scenario the bounce is correct, is the geometry at TH and therefore a volume expansion factor of the order to saturate dark matter, we need a densityplies of a verythe order ‘special’at state all. determining To the opposite, an initial it was low very en- highly crumpled. If 3 BOUNCING BLACK HOLESnot very IN far A BOUNCING from thethe epoch bounce UNIVERSE where had the far horizon more volume is Planck- and was not homogenous 2 of TH .Tohavethesu cient density of remnants today tropy. so, what is the origin of past low entropy, if it is not how Planckian PBH remands fromian, a which previous gives eon a linear(Penrose’sat all. expansion To EREBONS the opposite, factor) of the it was order3 very of highly crumpled. If special the initial geometry was? to saturate dark matter, we need a density of the order ⇢b ⇢TH TH But if the remnant(7) scenario is correct, the geometry at TH and therefore a volumeso, what expansion is the origin factor of of past⇠ the low order⇠ entropy, if it is not how Planck ofsize the particles matter can density pass⇢ troughM 3, and the this bounce. in turn is related to of gravity, Quintin, to which Brandenberger genericthe bounce evolution 1609.02556 had far tends, more are volume highly and was not homogenous 3 of TH .Tohavethesu atcient the density bounce. of Using remnants (4) we today haveCarr, anClifton, amount Coley of1704.02919 internal ⇢bTH by⇢T4H the FriedmannTH equation (7) special the initialcrumpled, geometry notwas? homogeneous. (For interesting criticisms We want⇠ Mo ≥ ⇠tHubble for them to survive till today. at all. To the opposite, it was very highly crumpled. If to saturate dark matter,volume we need per a unit densityand of external informed of the order volume alternative perspectives, see [38–41].) 2 so, what is the origin of past lowIV. entropy, PERSPECTIVAL if it is not how ENTROPY at the bounce. Using (4) we have an amount1 ofa˙ internal 3 The fact that source2 of past low entropy, hence the Inflation dilutes PBH: ⇢M , ⇢b ⇢T (5)TH Vint = ⇢bVWH(7)>TH .special the initial(8) geometry was? volume per unit of external volume T 2 ⇠ a ⇠ ⇠ H ⇠ source of irreversibility, was the homogeneity of space H ✓ ◆ IV. PERSPECTIVAL ENTROPY An imposing aspects of the Cosmos is the mighty daily is confirmed by a simple analysis of the thermodynam- 2 at the bounce. Using (4This) we means have an that amount only a of fraction internal rotation of Sun, Moon, planets, stars and all galaxies Vintwhere= ⇢bVWH we neglect>TH . factors of order(8) unit. Therefore the ical history of the universe. For instance irreversibility volume per unit of external volume 2 120 around us. Why does the Cosmos rotate so? Well, it is PAST currentLOW ENTROPY density ⇢ of remnants is of the orderAn imposing aspectson Earth1 of/T the is Cosmos10 due to theis the strong mightyIV. source daily(9) PERSPECTIVAL of negative en- ENTROPY This means that only a fraction H ⇠ not the Cosmos rotating, it is us. The rotation of the sky V rotation= ⇢ V of Sun,>T2 . Moon,ergy formed planets, by(8) the stars sun; and the sun all galaxies in turn was irreversibly Matter near thermal equilibrium: geometry1 hasint lowof entropyb theWH volume H of the universe was outside the remnants at is a perspectival phenomenon: we understand it better as 2 120 ⇢ ⇢M 2 . around us.(6) Why doesformed the by Cosmos the collapse rotate of a so? primordial Well, it cloud is under grav- Only 1 /T 10 of the ⇠volume⇠ ofT (9)the universethe was bounce. outside If the we assumeremnants equiprobability at the bounce!An for imposing each equal aspectsdue of to the the Cosmos peculiarity is the of mighty our own daily moving point of view, H This meansH that onlynot a the fraction Cosmos rotating,itational it attraction. is us. The Therefore rotation of the the original sky negative en- ⇠ volume of the universe, the probabilityrotation for an observer of Sun, to Moon,rather planets, than as stars a global and feature all galaxies of all celestial objects. If we take the mass of each remnant tois be a perspectival Planckian phenomenon:tropy driving we irreversibility understand around it better us as canThe be traced list of to conspicuous phenomena that have turned out of the volume of the universe was outside the remnants at 1/Tbe2 outside10 120 those remnants at the(9) bouncearound is one us. part Why in does the Cosmos rotate so? Well, it is [15], namely of order unit in Planck units,due⇢ isH to also120 the their peculiaritythe early of our lack own of gravitational moving point clumping. of view, Asto repeatedly be perspectival is long; recognising them has been a the bounce. IfPlanck we assume Stars equiprobability for each equal 10 ⇠. Therefore an observer outside thenotFrancesca remnants the Cosmos Vidotto is in rotating, it is us. The rotation of the sky number density in the units we are using.rather From than the big as apointed global feature out by Penrose, of all120 celestial the fact objects. that thepersistent geometry aspect of of the progress of science. volume of the universe, the probability forof an the observer volume to of the universethis sense was outside ‘special’ the as remnantsone part in at 10 is. a perspectival phenomenon: we understand it better as bounce to the current epoch the universe has widely ex- the universe was small and homogenous to the degree re- be outside those remnants at the bouncethe is one bounce. part If in we assumeThe list equiprobability of conspicuous for phenomena each equal thatdue have to turned the peculiarity out ofThe our hypothesis own moving put forward point of in view, [26] is that the increase panded. Assuming at least 60 e-folding, the bounce is quired by the current standard cosmologicalof model, entropy im- is a perspectival phenomenon in this sense. To 10120. Therefore an observer outside thevolume remnants of the is in universe,to be the perspectival probability for is long;an observer recognising to rather them has than been as a a global feature of all celestial objects. not very far from the epoch where the horizon is Planck- plies a very ‘special’ state determining an initial low en- this sense ‘special’ as one part in 10120. persistent aspectIII. of the PAST progress LOW ENTROPY of science.The list of conspicuousbe sure, phenomena it is not that subjective have turned or mental, out or illusory. Rather, ian, which gives a linearbe outside expansion those factor remnants of the order at the of bouncetropy. is one part in its source is in the relation between an observer system 120 The hypothesis put forward in [26] isto that be the perspectival increase is long; recognising them has been a T and therefore a volume10 . expansion Therefore factor an observer of the order outside theBut remnants if the remnant is in scenario is correct, theand geometry an observed at system, like for the rotation of the sky. H of entropyThe mystery is a perspectival120 of the second phenomenon principlepersistent of in thermodynam- this sense. aspect To of the progress of science. of T 3 .Tohavethesuthis cient sense density ‘special’ of remnantsas one part today in 10 the. bounce had far more volume and was not homogenousThis is possible because the entropy of a system de- III. PAST LOWH ENTROPY be sure,ics is it not is whynot subjective entropy growth or mental, towards or the illusory.The future. hypothesis Rather, That’s put forward in [26] is that the increase to saturate dark matter, we need a density of the order at all. To the opposite, it was very highly crumpled.pends on the If system’s microstate but also on the coarse its sourcepretty obvious. is in the The relation mystery between is why an entropyof observer entropy diminishes is system a perspectival phenomenon in this sense. To going towards theso, what past [ is30 the–35]. origin All current of past lowirreversible entropy, ifgraining it is not how under which the system interacts. The relevant 3 III. PASTand an LOW observed ENTROPY system, like for the rotationbe sure, of it the is not sky. subjective or mental, or illusory. Rather, The mystery of the second principle of⇢ thermodynam-b ⇢TH TH phenomena,(7) includingspecial our the own initial future-oriented geometry was? thinking, coarse graining is determined by the concrete existing ⇠ ⇠ its source is in the relation between an observer system ics is not why entropy growth towards the future. That’s Thisthe existenceis possible of because memories the and entropy the direction of a system of causal- de- interactions with the system. The entropy we assign to at the bounce. Using (4) we have an amount of internal pretty obvious. The mystery is why entropyThe diminishes mystery of thepends secondity on we principle the use system’sto make of thermodynam- sense microstate of the world,but alsoand canon an be theobserved traced coarse to system,systems like around for the us rotation depends of on the the sky. way we interact with volume per unit of external volume This is possible because the entropy of a system de- going towards the past [30–35]. All currentics is irreversible not why entropygraining growththe fact under towards that which entropy the future. the was systemIV. low That’s in PERSPECTIVAL interacts. the past [36 The, 37]. relevant SinceENTROPYthem – as the apparent motion of the sky depends on our pretty obvious. The mysterymatter is was why apparently entropy diminishes near thermal equilibriumpends on the in the system’sown microstate motion. but also on the coarse phenomena, including our own future-orientedV = ⇢ V thinking,>T2 . coarse graining(8) is determined by the concrete existing intgoingb towardsWH H the pastinteractionspast, [30–35 the]. lowwith All entropy current the system. was irreversible concentrated The entropygraining on the we geometry. assign under which to theThis system observation interacts. opens The a novel relevant way for facing the puz- the existence of memories and the direction of causal- An imposing aspects of the Cosmos is the mighty daily phenomena, includingsystems ourIn fact, own around future-oriented in standard us depends cosmology thinking, on the geometry waycoarsewe isinteract assumed graining with to is determinedzle of the arrow by the of concrete time: the existing universe is in a generic ity we use to make senseThis of means the world, that only can a be fraction traced to rotation of Sun, Moon, planets, stars and all galaxies the existence of memoriesthembe – nearly asand the the homogenous. apparent direction motion of For causal- the of the gravitational skyinteractions depends field, on with ho- our thestate, system. but The su ciently entropy rich we to assign include to subsystems whose the fact that entropy was low in the past [362, 37]. Since120 around us. Why does the Cosmos rotate so? Well, it is 1ity/T we use10 to make sensemogeneity of the(9) world, is a very can low be traced entropy to configuration,systems around because us dependscoupling on defines the way a coarsewe interact graining with for which entropy in- matter was apparently near thermal equilibriumH ⇠ in the own motion. not the Cosmos rotating, it is us. The rotation of the sky the fact that entropy wasgravity low in tends the past to clump [36, 37 and]. genericallySince them the evolution – as the apparent of creases motion monotonically. of the sky depends These subsystems on our are those where past, the low entropy was concentrated on the geometry. This observationis opens a perspectival a novelphenomenon: way for facing we the understand puz- it better as of the volume of the universematter was was outside apparently the remnantsperturbations near thermal at leads equilibrium increasingly in the awayown from motion. homogene- information can pile up and ‘information gathering crea- In fact, in standard cosmology geometry is assumed to zle of the arrowdue of time: to the the peculiarity universe of is our in own a generic moving point of view, the bounce. If we assumepast, equiprobability the low entropy for wasity. each concentrated In equal fact, as longon the argued geometry. by Penrose,This generic observation states openstures’ a such novel as way those for composing facing the the puz- biosphere can exist. be nearly homogenous.volume For of the the gravitational universe, the field,probability ho- forstate, an observer but su to cientlyrather rich than to as include a global subsystems feature of whose all celestial objects. mogeneity is a very low entropy configuration,In fact, because in standardcoupling cosmology defines geometry aThe coarse is list assumed of graining conspicuous to for whichzle phenomena of entropy the arrow that in- have of time: turned the out universe is in a generic be outside those remnantsbe nearly at the homogenous. bounce is one For part the in gravitational field, ho- state, but su ciently rich to include subsystems whose gravity tends to clump120 and generically the evolution of creases monotonically.to be These perspectival subsystems is long; are recognising those where them has been a 10 . Therefore an observermogeneity outside is a very the remnants low entropy is in configuration, because coupling defines a coarse graining for which entropy in- perturbations leads increasinglythis sense ‘special’ away as from one homogene- part in 10120. information can pilepersistent up and aspect ‘information of the progress gathering of science. crea- gravity tends to clump and generically the evolution of creases monotonically. These subsystems are those where ity. In fact, as long argued by Penrose, generic states tures’ such as thoseThe composing hypothesis the put biosphere forward can in [26 exist.] is that the increase perturbations leads increasingly awayof from entropy homogene- is a perspectivalinformation phenomenon can pile in this up sense. and ‘information To gathering crea- III. PASTity. LOW In fact, ENTROPY as long argued by Penrose,be sure, generic it is notstates subjectivetures’ or such mental, as thoseor illusory. composing Rather, the biosphere can exist. its source is in the relation between an observer system The mystery of the second principle of thermodynam- and an observed system, like for the rotation of the sky. ics is not why entropy growth towards the future. That’s This is possible because the entropy of a system de- pretty obvious. The mystery is why entropy diminishes pends on the system’s microstate but also on the coarse going towards the past [30–35]. All current irreversible graining under which the system interacts. The relevant phenomena, including our own future-oriented thinking, coarse graining is determined by the concrete existing the existence of memories and the direction of causal- interactions with the system. The entropy we assign to ity we use to make sense of the world, can be traced to systems around us depends on the way we interact with the fact that entropy was low in the past [36, 37]. Since them – as the apparent motion of the sky depends on our matter was apparently near thermal equilibrium in the own motion. past, the low entropy was concentrated on the geometry. This observation opens a novel way for facing the puz- In fact, in standard cosmology geometry is assumed to zle of the arrow of time: the universe is in a generic be nearly homogenous. For the gravitational field, ho- state, but su ciently rich to include subsystems whose mogeneity is a very low entropy configuration, because coupling defines a coarse graining for which entropy in- gravity tends to clump and generically the evolution of creases monotonically. These subsystems are those where perturbations leads increasingly away from homogene- information can pile up and ‘information gathering crea- ity. In fact, as long argued by Penrose, generic states tures’ such as those composing the biosphere can exist. Scenario 2
Quantum Black Holes Francesca Vidotto 2 4 mal extension of the Schwarzschild solution is equally the 2 orthogonal statesoutside in of the a common black hole Hilbert and the space outside˜ of of the a white hole3. Hawking evaporation quantum states(see of Fig. geometry 1, Top). and Analogous matter inside considerations aH sphere, hold for the Kerr solution. In other words, the continuation inside mal extension of the Schwarzschildof Schwarzschild solution radius isr equally=2m.Thisisareducedmodel the B, m, v B,m m, v . (14) the radius r =2m + ✏ of an external stationary black
outside of a black holesince and we the disregard outside of internal a white degrees hole of freedom others | i!| i hole metric contains both a trapped region (a black hole) WH II (see Fig. 1, Top). Analogousthan v. We considerations are interested hold in for the the evolution of the state This is a process that decreases the mass of a black ad an anti-trapped region (a white hole). BH Kerr solution. In otheras the words, surface the⌃ continuationmoves up in time. inside hole, produced by negative energy entering the hole the radius r =2m + ✏ of an externalWhatstationary distinguishesblack then a black hole from a white
hole? The objects in the sky we call ‘black holes’ are de-when a Hawking quantum is radiated. It is a phe- hole metric contains both a trapped region (a black hole) WH II Let’s labelscribed the position by a of stationary⌃ with a metric temporal only parameter approximately, andnomenon described by the classical backreaction on ad an anti-trapped region (a white hole). BH t. For a blackfor hole, a limited it is time.natural In to their identify pastt (atwith least) the their met-the geometry of the dynamics of a quantum field. What distinguishes then a black hole from a white advanced timeric v was and definitely for a white non-stationary, hole, it is as natural they were to producedHawking radiation theory gives hole? The objects inidentify the sky itwe with callby gravitational‘blackthe retarded holes’ are collapse.time de- -u. So In let’s this case, define the continuation scribed by a stationary metric onlyof the approximately, metric inside and the radius r =2m + ✏ contains a dm ~ FIG. 2: The= full. life of a black-white(15) hole. for a limited time. Indt= theirdv, pastfortrappedH (at= least)B, region,and their butdt= met- notd anu, anti-trappedfor H = W, region(7) (see Fig. dt m2 ric was definitely non-stationary,1, as Center). they were Viceversa, produced a white hole is an object that is Giving the lifetime for a massive black hole by gravitational collapse.with an In arbitrary thisundistinguishable case, origin the continuation for the from t label. a black hole from the exterior and is longer [16]: of the metric inside theA radius numberrfor=2 of a processes finitem + time,✏ contains can but occur in a the asfuture the ceases surface to be⌃ stationary FIG. 2: The full life of a black-white hole. 3 and there is no trapped region in its future (see Fig. 1, m 4 trapped region, but notmoves an upanti-trapped in time. region (see Fig. ⌧B .⌧BH mo. (16) (2) 1, Center). Viceversa,We a white list them holeBottom). is here an using object relativistic that is units G = c =1 ⇠ ~ ⇠ The tunnelling process itself from black to white takes a undistinguishable fromand a black keeping hole~ explicit from the to exterior distinguish and classicalis longer from [16 quan-]: for a finite time, buttum in the phenomena. future ceases to be stationary 4. Blacktime to white of the tunnelling order of the current mass at transition time III. QUANTUM PROCESSES AND TIME [415]. The area of the horizon of the black hole decreases and there is no trapped region in its future (see Fig. 1, ⌧BH mo. (2) 1. Black hole volume increase andSCALES white hole volume ⇠ with timeB, m, because v ofW, Hawking m, v . evaporation,(17) decreasing Bottom). | i!| i decrease The tunnelling process itself fromfrom blackmo toto white the Planck takes a mass mPl. At this point the transition happens and a white hole of mass of the order The classical prediction thattime the of black the order is forever of the stable currentThis is mass a genuine at transition quantum time gravitational process B, m, v B, m, v + v , (8) [16, 30of, the31]. Planck Its probability mass is formed. per unit of time is still III. QUANTUM PROCESSESis| not AND reliable.i! TIME| In the uppermost[15i ]. The band area of of the the central horizon of the black hole decreases unclear. We take here the conservative estimate de- SCALES diagramW, m, v of Fig. 1W, quantum m, v theoryvwith. time dominates. because(9) The of death Hawking evaporation, decreasing of| a blacki! hole is| therefore a quantumi phenomenon. Therived in [15] using covariant Loop Quantum Grav- from mo to the Planck mass mPl. At this pointIV. the TIMESCALES This issame simply is true determined for a white by the hole,transition Einstein’s reversing happens equa- time direction. and a whiteity [32 hole], which of mass agrees of the with order the semiclassical expec- The classical prediction thattions the ifThat nothing black is, is elsethe forever birthhappens. stable of a The white variation hole is is in com- a region wheretation for tunnelling phenomena, namely that this of the Planck mass is formed. Consider the hypothesis that white-hole remnants are is not reliable. In the uppermostputed inquantum [ band26] to of gravitationalbe the governed central by phenomena are strong. probability is suppressed by the semiclassical stan- a constituent of dark matter. To give an idea of the diagram of Fig. 1 quantum theory dominates.This consideration The death eliminates a traditional objectiondard tunnelling factor dv density of these objects, a local dark matter density of of a black hole is therefore a quantumto the phenomenon. physical existence The2 of white holes: How wouldIV. TIMESCALESthey 3 = 3p3⇡mo. (10) the order of 0.01M /pc2 corresponds to approximately same is true for a white hole, reversingoriginate?d timet They± direction. originate from a region where quantum S m one Planck-scalee ~ remnant,e ~ with the weight(18) of half a inch That is, the birth of a white holephenomena is in a region dominate where the behaviour of the gravitational 5 of human hair, per⇠ each 10.000Km3. For these objects to quantum gravitational phenomenawhere mfield.o areis strong. the initial mass of the blackConsider hole the and hypothesis that white-hole remnants are a constituent of dark matter.wherebe ToS stillis give a presenttypical an idea action now of we for the need the that transition. their lifetime On di- be larger This consideration eliminatesthegoverned sign a is traditionalSuch by plus the regions for Hamiltonian a black objection are hole generated and minus in particular for white by the endwhere we have taken the Immirzi parameter to be unit mensionalor equal grounds, than the this Hubble suggests time a tunnellingTH , that is prob- hole. of the life of a black hole,2 asdensity mentioned of these above. objects, Hencefor a local simplicity. dark matter The minimal density non-vanishing of eigenvalue is to the physical existence of white holes: Howp would2 @ they~ @ ~ 3 ability per unit time am white+3 hole3 i⇡m cano @v in principlei m2 @mthe be order originatedb ofm 0.01 byM a/pc dyingcorresponds to approximately4 originate? They originate from a region where quantum mo TH . (3) 2. WhiteH = toblack black hole. instability This scenario hasone been Planck-scale shown to be remnant, concretely with the weight ofa half=4 ap inch3⇡ G (24) 0 2 1 o m2 ~ phenomena dominate the behaviour of the gravitational~ m /~ p 2 @ 3 compatiblec m withe the exactof externalm human3 Einstein3 hair,i⇡m pero @v dynamics each 10.000KmOn the. For other thesep hand, objectse ~ since/m to the possibility of(19) many larger field. ⇠ @in [12W,] and m, v has beenB, m, explored v . be still in [ present13–18(11)]. now The(22)A we causal needand that isback called their holes the lifetime is ‘area constrained be gap’ larger in loop by observation, quantum cosmology we5 expect rem- Such regions are generated in particular| byi! the| end i wherediagram we have added of the also spacetime a diagonal givingor energy equal the full than term life propor-the cycle Hubble of the[42 timeHere]. ThisTnants we, gives thathave to be is a assumed minimal produced for non-vanishing by simplicity already evaporated that mass theµ defined in- black holes, of the life of a black hole,This as mentioned process is allowed above. by Hence classical general relativ- H 2 2 governedtional byblack-white to the the Hamiltonian mass inhole order is given to obtain below the in standard Fig. 2. energywherebyternal weao have=therefore volume 16⇡ takenG µ thev, theis that lifetime conserved Immirzi is of parameter the in this black transition. hole to be must unit A be shorter a white hole can in principleityphase in be the evolution, originatedIn absence particular, and of by anyc a theand dyingperturbation resultb are of constants [16] when indicates of there order that is unit. the black-4 than the Hubble time. Therefore 2 form simplicity.o moreTH precise. The account minimal of non-vanishing this1 (3) process eigenvalue will be studied is black hole. This scenario hasa second beenWe now shown asymptotic ask to what be2 @ concretely region,are the~ as stable@ it is or apparent semi-stable~ from states 3 4 m +3to-whitep3 i⇡m process isi asymmetric2 inb time [13] and the timeelsewhere (for the tentative phenomenology~ derived o @v m @m m µ 3 . (25) compatible with the exactH =theof external the Topscales hole panel Einsteinas of of seen the Fig. fromdurations dynamics3; but the it exterior of can theOn also. di↵ the beerent triggered other phases hand, are since deter- thefrom possibility this process, ofa many=4 seep⌘ [333 larger⇡2–39Gm]).oG
Quantum Black Holes Francesca Vidotto UNIVERSALITY OF BLACK HOLE EXPLOSION?
LARGE EXTRA DIMENSIONS
1st order topological phase transition from black string to black hole Casadio and Harms 2000/01 Gubser 2002, Kol 2002 occurring because of the Gregory-Laflamme metrical instability Gregory and Laflamme 2002
BRANES Large black holes localized on infinite Randall-Sundrum branes:
period of rapid decay via Hawking radiation of CFT modes Emparana, Garcıa-Bellido, Kaloper 2003
Quantum effects shorten the lifetime of black holes!
Quantum Gravity Phenomenology Francesca Vidotto FIREWALL NO-GO THEOREM
Assumptions: Almheiri, Marolf, Polchinski, Sully 1207.3123 General Relativity: Equivalence Principle Quantum Mechanics: Unitary Evolution QFT in Curved Spacetime (fixed background)
Firewall argument after the Page time i.e. when about half of black-hole mass has evaporated particles emitted needs to break entanglement releasing an enormous energy
Black Hole Lifetime Vidotto, Rovelli 1401.6562 Quantum Gravity effects should manifest before the Page time ⟹ the hole lifetime must be shorter or of the order of ~ m3
See also Quantum Break Time Dvali, Gomez 1112.3359
Planck Stars Francesca Vidotto BLACK-HOLE LIFETIME
For something quantum to happens, semiclassical approximation must fail.
Typically in quantum gravity: high curvature Curvature ~ (LP)-2 Small effects can pile up: small probability per time unit gives a probable effect on a long time!
Typically in quantum tunneling: Curvature × (time) ~ (LP)-1
Haggard, Rovelli 1407.0989
Chistodoulou, Rovelli, Speziale, Vilensky 1605.05268
Planck Stars Francesca Vidotto BLACK-HOLE LIFETIME
For something quantum to happens, semiclassical approximation must fail.
Typically in quantum gravity: high curvature Curvature ~ (LP)-2 Small effects can pile up: small probability per time unit gives a probable effect on a long time!
Typically in quantum tunneling: Curvature × (time) ~ (LP)-1 m T 1 r3 b ⇠
Haggard, Rovelli 1407.0989
Chistodoulou, Rovelli, Speziale, Vilensky 1605.05268
Planck Stars Francesca Vidotto BLACK-HOLE LIFETIME
For something quantum to happens, semiclassical approximation must fail.
Typically in quantum gravity: high curvature Curvature ~ (LP)-2 Small effects can pile up: small probability per time unit gives a probable effect on a long time!
Typically in quantum tunneling: Curvature × (time) ~ (LP)-1 1m TT 1 mr23 b ⇠ ⟹ the hole lifetime must be longer or of the order of ~ m2
Haggard, Rovelli 1407.0989
Chistodoulou, Rovelli, Speziale, Vilensky 1605.05268
Planck Stars Francesca Vidotto BLACK-HOLE LIFETIME
For something quantum to happens, semiclassical approximation must fail.
Typically in quantum gravity: high curvature Curvature ~ (LP)-2 Small effects can pile up: small probability per time unit gives a probable effect on a long time!
Typically in quantum tunneling: Curvature × (time) ~ (LP)-1 1m TT 1 mr23 b ⇠ ⟹ the hole lifetime must be longer or of the order of ~ m2
Haggard, Rovelli 1407.0989
Black-to-White Tunnelling In the quantum world, things happen as soon as they can! Indications from a full LQG computations.
Chistodoulou, Rovelli, Speziale, Vilensky 1605.05268
Planck Stars Francesca Vidotto NON-SINGULAR BLACK HOLES
QUANTUM REPULSION Non-perturbative effect Effective theory: quantum repulsion
TIME DILATATION Bounce time ~ M ~ ms for M 2 9 Asymptotic time ~ M ~10 for M
LIFETIME ~ M2 to be compared with the evaporation time ~ M3 (no information paradox)
Quantum BlackGravity Holes Phenomenology Francesca Vidotto Can we observe it?
Quantum Black Holes Francesca Vidotto PRIMORDIAL BLACK HOLES
All black holes are subject to quantum effects.
An explosion observed today, requires old black holes: primordial.
(Quantum) PBH dark matter:
Today, black holes smaller than m ( t ) t = t have already exploded. | H It decreases with time. ( but for later accretion/merging )
Caution with constraints! Constraints from Hawking evaporation do not apply. PBH could exists, but not necessarily constitute all DM.
Quantum Gravity Phenomenology Francesca Vidotto QUANTUM PRIMORDIAL BLACK HOLES AS DARK MATTER
Structure formation Bellomo, Bernal, Chluba, Cholis, Raccanelli, Verde, Vidotto WIP
Result: Planck Stars compatible with constraints from early cosmology
First stars & Supermassive black holes
Primordial black holes inside first-generation stars can provide the seeds for supermassive black holes.
Quantum Gravity Phenomenology Francesca Vidotto EFFECTS IN THE LATE UNIVERSE
Raccanelli, Vidotto, Verde 1708.02588
1 A 8 B +BCA B B 04 G 2,0 9 G
G 3/ BCA6 CB DBC8A 45 8 B 2A8 DB BCA6 CB
G G G G G G 1 1H
Quantum Gravity Phenomenology Francesca Vidotto 3 where refers to the overdensity in the comoving gauge, magnified and become detectable, so that the observed rsd and v denote Doppler effects and peculiar velocity number density of sources increases. At the same time, [49], the lensing convergence and pot incorporates lo- the stretching of the field of view leads to a decrease of cal and non local terms depending on Bardeen potentials the observed number density. The combined effect can and their temporal derivatives; t includes tensor pertur- be written as: bation effects. For simplicity, we omitted the redshift and nobs(z)=n (z)[1 + (5s 2)] , (6) direction dependencies (n,z). g Galaxy clustering measurements have been used to obs where n and ng are the observed and intrinsic number measure cosmological parameters for a variety of cosmo- of sources, respectively, s is the magnification bias and logical models (see e.g. [50–56]), and it is the focus of is the convergence. The net modification of the observed many future large scale galaxy surveys (see e.g. [57–61]). number density is called magnification bias s: Therefore it is interesting to see that it can also be used to test different QG models and potentially extend con- d logN `m `m , with `m denoting the spherical harmon- 2 2 Y perturbedY by peculiar velocities, ics functions, n the direction on the sky and zi is the red- cross-correlating galaxies in two disjoint redshift bins (see P gravitational lensing and potentials e.g. [69, 70]).0, ,4 1 shift. This can be calculated from the underlying matter 0, ,4 1 6 power spectrum by using: 0, ,4 1 4⇡dk C. Galaxy surveys CXY (z ,z )= 2(k) W X(k, z ) W Y(k, z ) , (4) ` i j k ` i ` j Z We model our galaxy 6 6 survey after the Square Kilo- X,YChoice of redshift distribution: 2 where W`{ } are the source distribution kernels for the metre Array (SKA) , which is an international multi- different observables (i.e. galaxies in different redshift purpose 7 next-generation radio interferometer, that will 2 1.+ 265 35884 0 bins) and (k) )is the dimensionless matter power spec- be built in the Southern Hemisphere in Africa and in trum today. Australia, with a total collecting area of about 1 km2. 88 , 7 The kernel for the galaxy clustering can be written as Among many types of observations delivered by such in- (see e.g. [62]): struments, , 0 we focus here on surveys that will detect in- 2 1 5 31 dividual galaxies2 1 in the 5 3 radio1 continuum [71]; we assume 2 X dNX (z) ( 7 that the survey2 1 will cover 5 31 30 , 000 deg ,andwecompute W` (k)= D(z) bX(z) )j`[k ( z)] dz , (5) dz 1µJy Z results for a flux limit of .Althoughradiocontin- uum surveys do not have in principle redshift informa- where dN (z)/dz is the objects redshift distribution, X tion, some techniques have been proposed to allow the D(z) theQuantum growth Gravity rate Phenomenology of structures, b (z) is the bias Francesca Vidotto X possibility to divide the galaxy catalog into tomographic that relates the observed overdensity to the underlying redshift bins; here we follow the clustering-based redshift matter distribution (see [63] for a recent review); j (x) ` (CBR) information approach proposed in [72], and stud- is the spherical Bessel function of order `,and (z) is ied for some cosmological applications (including some the comoving distance. predictions for the SKA), in [73]. In Figure 1 we show the (normalized) redshift distribution for the SKA radio continuum survey we use for this paper. We compute the observational consequences of BH de- B. Cosmic Magnification cay by using a modified version of the class3 code, and we investigate the effects on galaxy angular power spec- Gravitational lensing causes the deflection of light rays tra. Given the specifications of the proposed future sur- by the matter distribution along the line of sight, causing veys, we forecast the measurements’ precision using the two competing effects: on one hand, a size magnification of sources behind a lens, on the other hand lensing causes the stretching of the observed field of view. Therefore, for magnitude (or flux) limited galaxy surveys, sources 2 https://skatelescope.org that are just below the threshold for detection will be 3 http://class-code.net/ EXPECTED SIGNALS Barrau, Rovelli, Vidotto 1409.4031 fast process ( few milliseconds? ) the source disappears with the burst very compact object: big flux E = mc2 1.7 1047 erg ⇠ ⇥ tH 2Gm exploding today: m = 1.2 1023 kg R = 2 .02 cm r 4k ⇠ ⇥ c ⇠ 2Gm LOW ENERGY: size of the source ≈ wavelengthR = predicted & . 02 . 05 cm cm (?) c2 ⇠ HIGH ENERGY: energy of the particle liberated Tev ⇡ SYNCHROTRON EMISSION Kavic &al. 0801.4023 GRAVITATIONAL WAVES Quantum Gravity Phenomenology Francesca Vidotto FAST RADIO BURSTS fast process ( few milliseconds ) compact object: big flux E = mc2 1.7 1047 erg ⇠ ⇥ HIGH ENERGY Tev ➞ REES’ MECHANISM Kavic &al. 0801.4023 ⇡ Electron-positron pairs traveling trough a magnetic field Repetition can be due to: • reflection of the signal due to plasm walls • region dense of PBH 2Gm LOW ENERGY: size of the source ≈ wavelength R = . 02. 05 cm cm predictedc2 ⇠& We may have missed a factor in our rough calculation! We may be seeing only the a window in a distribution of event Barrau &al. 1801.03841 Quantum Gravity Phenomenology Francesca Vidotto MAXIMAL DISTANCE Barrau, Bolliet, Vidotto, Weimer 1507.1198 shorter lifetime — smaller wavelength Low energy channel High energy channel 1024 1028 1022 26 Hubble radius 10 Galactic scale ] ] 1020 m m 24 [ [ 10 R R Hadron decay 1018 1022 Galactic scale Direct emission 1016 1020 k 1 104 108 1012 1016 1020 k 1 104 108 1012 1016 1020 E [eV] 2.7 2.7×102 2.7×104 2.7×106 2.7×108 E [eV] 3.6×1013 3.6×1014 3.6×1015 3.6×1016 3.6×1017 detection of arbitrarily far signals PBH: mass - temperature relation better single-event detection different scaling Quantum Gravity Phenomenology Francesca Vidotto THE SMOKING GUN: DISTANCE/ENERGY RELATION Low energy channel distant signals originated in younger and smaller sources Quantum Gravity Phenomenology Francesca Vidotto THE SMOKING GUN: DISTANCE/ENERGY RELATION Low energy channel distant signals originated in younger and smaller sources Quantum Gravity Phenomenology Francesca Vidotto THE SMOKING GUN: DISTANCE/ENERGY RELATION Low energy channel distant signals originated in younger and smaller sources Quantum Gravity Phenomenology Francesca Vidotto maximal extension of the Schwarzschild metric for a The energy (and amplitude) of the signal emitted in mass M. Region (III) is where quantum gravity becomes the quantum gravity model considered here remains non-negligible. open. As suggested in [11] and to remain general, we consider two possible signals of di↵erent origins. Importantly, by gluing together the di↵erent part of The first one, referred to as the low energy signal, the e↵ective metric and estimating the time needed for is determined by dimensional arguments. When the maximal extension of the Schwarzschildquantum e↵ects metric to happen, for a it wasThe shown energy that the (and dura- amplitude)bounce of is the completed, signal emitted the black in hole (more precisely the mass M. Region (III) is wheretion quantum of the gravity bounce becomes should not bethe shorter quantum than [10] gravity modelemerging considered white hole) here has remains a size (L 2M)determinedby non-negligible. open. As suggested inits [11] mass andM. to This remain is the general, main scale⇠ of the problem and it ⌧ =4kM2we, consider two possible(1) fixes signals an expected of di↵erent wavelength origins. for the emitted radiation: The first one, referred to asL the. Welow assume energy thatsignal, particles are emitted at the Importantly, by gluing together the di↵erent part of ⇠ the e↵ective metric and estimatingwith k> the time0.05 needed a dimensionless for is parameter. determined We by dimensional use prorata arguments. of their number When of internal the degrees of freedom. Planck units where G = ~ =bouncec = 1. is completed, The bounce the black(This hole is also (more the case precisely for the the Hawking spectrum at the quantum e↵ects to happen, it was shown that the dura-2 3 tion of the bounce should nottime be shorter is proportional than [10] to M andemerging not to M whiteas hole) in the has aoptical size (L limit,2Mi.e.)determinedbywhen the greybody factors describ- Hawking process. As long as kitsremains mass M small. This enough, is the maining scalethe backscattering⇠ of the problem probability and it are spin-independent.) the bounce time is much smaller than the Hawking 2 fixes an expectedTHE wavelength SMOKING for GUN: the emitted DISTANCE/ENERGY radiation: RELATION ⌧ =4kMevaporation, time and the(1) evaporation can be considered The second signal, referred to as the high energy com- L. We assume that particles are emitted at the as a dissipative correction that can⇠ be neglected in a ponent, has a very di↵erent origin. Consider the history with k>0.05 a dimensionlessfirst order parameter. approximation. We use prorata of their number ofof internal the matter degrees emerging of freedom. from a white hole: it comes from Planck units where G = ~ = c = 1. The bounce (This is also the case forHigh the energy bounce Hawking channel of thespectrum matter at that the formed the black hole by 2 3 time is proportional to M andThe not phenomenology to M as in was the investigatedoptical in limit, [11] underi.e. thewhen thecollapsing. greybody In most factors scenarios describ- there is a direct relation be- Hawking process. As long asassumptionk remains that smallk takes enough, its smallesting possible the backscattering value, which probabilitytween the are formation spin-independent.) of a primordial black hole of mass M the bounce time is much smallermakes the than bounce the Hawking time as short as possible. The aim and the temperature of the Universe when it was formed evaporation time and the evaporationof the present can be article considered is to go beyondThe this second first signal, study in referred(see to [14] as for the ahigh review). energyM com-is given by the horizon mass as a dissipative correction thattwo can directions. be neglected First, we in generalize a ponent, the previous has a very results di↵erentMH origin.: Consider the history by varying k. The only conditionof the for matter the model emerging to be from a white hole: it comes from first order approximation. M M t. (2) valid is that the bounce time remainsthe bounce (much) of the smaller matter that formed the black⇠ holeH by⇠ than the Hawking time. This assumption is supported The phenomenology was investigated in [11] under the collapsing. In most scenarios(Other there more is a direct exotic relation models, be-e.g. collisions of cosmic by the “firewall argument” presented in [1]. We study in tween the formation of a primordialstrings or black collisions hole of of bubbles mass M associated with di↵erent assumption that k takes its smallestdetail possible the maximal value, distance which at which a single black-hole vacua, can lead to di↵erent masses at a given cosmic time. makes the bounce time as shortbounce as possible. can be detected. The aim Second,and we go the beyond temperature this “sin- of the Universe when it was formed We will not consider them in this study.) The cosmic of the present article is to gogle beyond event this detection” first study and consider in (see the [14] di↵use for background a review). M is given by the horizon mass time t is related to the temperature of the Universe T by two directions. First, we generalizeproduced the by previous a distribution results of bouncingMH : black holes. by varying k. The only condition for the model to be 1 2 2 M MH t. t 0.3g (2)T , (3) valid is that the bounce time remains (much) smaller ⇠ ⇠ ⇠ ⇤ than the Hawking time. This assumptionII. SINGLE is supported EVENT DETECTION (Other more exotic models,wheree.g.g collisions100 is the of number cosmic of degrees of freedom. by the “firewall argument” presented in [1]. We study in ⇤ ⇠ strings or collisions of bubblesOnce associatedk is fixed, M with is fixed di↵ (byerent⌧ tH ) and T is therefore detail the maximal distance at which a single black-hole Quantum Gravity Phenomenology ⇠ Francesca Vidotto For detection purposes, wevacua, are interested can lead in to black di↵erentknown. masses at As a the given process cosmic is time. time-symmetric, what comes bounce can be detected. Second,holes we whose go beyond lifetime this is “sin- less than the age of the Universe. out from the white hole should be what went in the We will not consider them in this study.) The cosmic gle event detection” and considerFor the a primordial di↵use background black hole detected today, ⌧ = t black hole, re-emerging at the same energy: a blackbody time t is related to theH temperature of the Universe T by produced by a distribution of bouncingwhere tH is black the Hubble holes. time. This fixes the mass M, as spectrum at temperature T . Intuitively, the bouncing a function of the parameter k (defined in the previous black1 hole plays the role of a “time machine” that sends 2 2 section) for black holes that can be observed. Int all 0.3theg primordialT , universe radiation(3) to the future: while the ⇤ cases considered, M is very small compared to a solar⇠ surrounding space has cooled to 2.3K, the high-energy II. SINGLE EVENTmass DETECTION and therefore only primordialwhere blackg holes100 possibly is the numberradiation of emerges degrees from of freedom. the white hole with its original ⇤ ⇠ formed in the early Universe areOnce interestingk is fixed, from M is this fixed (byenergy.⌧ tH ) and T is therefore For detection purposes, wepoint are of interested view. Although in black no primordialknown. blackAs the hole process has is time-symmetric,⇠ what comes holes whose lifetime is less thanbeen the detected age of the to date, Universe. various mechanismout from for the their white pro- hole shouldWhen be the what parameter wentk inis taken the larger that its smallest For a primordial black holeduction detected shortly today, after⌧ the= t BigH Bangblack have hole, been re-emerging suggested atpossible the same value, energy: that a blackbodyis fixed for quantum e↵ects to be (see, e.g., [12] for an early detailed calculation and [13] important enough to lead to a bounce, the bounce time where tH is the Hubble time. This fixes the mass M, as spectrum at temperature T . Intuitively, the bouncing a function of the parameter kfor(defined a review). in the Although previous their numberblack hole density plays might the be role ofbecomes a “time larger machine” for a thatgiven sends mass. If this time is assumed way too small for direct detection, the production of to be equal to the Hubble time (or slightly less if we section) for black holes that can be observed. In all the primordial universe radiation to the future: while the primordial black holes remains a quite generic prediction focus on black holes bouncing far away), this means cases considered, M is very smallof cosmological compared to physics a solar eithersurrounding directly from space density has cooledthat to the 2.3K, mass thehas to high-energy be smaller. The resulting energy mass and therefore only primordialperturbations black holes –possibly possibly enhancedradiation by phase emerges transitions– from thewill white be higher hole with for both its original the low energy and the high formed in the early Universeor are through interesting exotic from phenomena this likeenergy. collisions of cosmic energy signals, but for di↵erent reasons. In the first point of view. Although no primordialstrings or bubbles black of hole false has vacua. case, because of the smaller size of the hole, leading been detected to date, various mechanism for their pro- When the parameter k isto taken a smaller larger emitted that its wavelength. smallest In the second case, duction shortly after the Big Bang have been suggested possible value, that is fixed for quantum e↵ects to be (see, e.g., [12] for an early detailed calculation and [13] important enough to lead to a bounce, the bounce time 2 for a review). Although their number density might be becomes larger for a given mass. If this time is assumed way too small for direct detection, the production of to be equal to the Hubble time (or slightly less if we primordial black holes remains a quite generic prediction focus on black holes bouncing far away), this means of cosmological physics either directly from density that the mass has to be smaller. The resulting energy perturbations –possibly enhanced by phase transitions– will be higher for both the low energy and the high or through exotic phenomena like collisions of cosmic energy signals, but for di↵erent reasons. In the first strings or bubbles of false vacua. case, because of the smaller size of the hole, leading to a smaller emitted wavelength. In the second case, 2 maximal extension of the Schwarzschild metric for a The energy (and amplitude) of the signal emitted in mass M. Region (III) is where quantum gravity becomes the quantum gravity model considered here remains non-negligible. open. As suggested in [11] and to remain general, we consider two possible signals of di↵erent origins. Importantly, by gluing together the di↵erent part of The first one, referred to as the low energy signal, the e↵ective metric and estimating the time needed for is determined by dimensional arguments. When the maximal extension of the Schwarzschildquantum e↵ects metric to happen, for a it wasThe shown energy that the (and dura- amplitude)bounce of is the completed, signal emitted the black in hole (more precisely the mass M. Region (III) is wheretion quantum of the gravity bounce becomes should not bethe shorter quantum than [10] gravity modelemerging considered white hole) here has remains a size (L 2M)determinedby non-negligible. open. As suggested inits [11] mass andM. to This remain is the general, main scale⇠ of the problem and it ⌧ =4kM2we, consider two possible(1) fixes signals an expected of di↵erent wavelength origins. for the emitted radiation: The first one, referred to asL the. Welow assume energy thatsignal, particles are emitted at the Importantly, by gluing together the di↵erent part of ⇠ the e↵ective metric and estimatingwith k> the time0.05 needed a dimensionless for is parameter. determined We by dimensional use prorata arguments. of their number When of internal the degrees of freedom. Planck units where G = ~ =bouncec = 1. is completed, The bounce the black(This hole is also (more the case precisely for the the Hawking spectrum at the quantum e↵ects to happen, it was shown that the dura-2 3 tion of the bounce should nottime be shorter is proportional than [10] to M andemerging not to M whiteas hole) in the has aoptical size (L limit,2Mi.e.)determinedbywhen the greybody factors describ- Hawking process. As long as kitsremains mass M small. This enough, is the maining scalethe backscattering⇠ of the problem probability and it are spin-independent.) the bounce time is much smaller than the Hawking 2 fixes an expectedTHE wavelength SMOKING for GUN: the emitted DISTANCE/ENERGY radiation: RELATION ⌧ =4kMevaporation, time and the(1) evaporation can be considered The second signal, referred to as the high energy com- L. We assume that particles are emitted at the as a dissipative correction that can⇠ be neglected in a ponent, has a very di↵erent origin. Consider the history with k>0.05 a dimensionlessfirst order parameter. approximation. We use prorata of their number ofof internal the matter degrees emerging of freedom. from a white hole: it comes from Planck units where G = ~ = c = 1. The bounce (This is also the case forHigh the energy bounce Hawking channel of thespectrum matter at that the formed the black hole by 2 3 time is proportional to M andThe not phenomenology to M as in was the investigatedoptical in limit, [11] underi.e. thewhen thecollapsing. greybody In most factors scenarios describ- there is a direct relation be- Hawking process. As long asassumptionk remains that smallk takes enough, its smallesting possible the backscattering value, which probabilitytween the are formation spin-independent.) of a primordial black hole of mass M the bounce time is much smallermakes the than bounce the Hawking time as short as possible. The aim and the temperature of the Universe when it was formed evaporation time and the evaporationof the present can be article considered is to go beyondThe this second first signal, study in referred(see to [14] as for the ahigh review). energyM com-is given by the horizon mass as a dissipative correction thattwo can directions. be neglected First, we in generalize a ponent, the previous has a very results di↵erentMH origin.: Consider the history by varying k. The only conditionof the for matter the model emerging to be from a white hole: it comes from first order approximation. M M t. (2) valid is that the bounce time remainsthe bounce (much) of the smaller matter that formed the black⇠ holeH by⇠ than the Hawking time. This assumption is supported The phenomenology was investigated in [11] under the collapsing. In most scenarios(Other there more is a direct exotic relation models, be-e.g. collisions of cosmic by the “firewall argument” presented in [1]. We study in tween the formation of a primordialstrings or black collisions hole of of bubbles mass M associated with di↵erent assumption that k takes its smallestdetail possible the maximal value, distance which at which a single black-hole vacua, can lead to di↵erent masses at a given cosmic time. makes the bounce time as shortbounce as possible. can be detected. The aim Second,and we go the beyond temperature this “sin- of the Universe when it was formed We will not consider them in this study.) The cosmic of the present article is to gogle beyond event this detection” first study and consider in (see the [14] di↵use for background a review). M is given by the horizon mass time t is related to the temperature of the Universe T by two directions. First, we generalizeproduced the by previous a distribution results of bouncingMH : black holes. by varying k. The only condition for the model to be 1 2 2 M MH t. t 0.3g (2)T , (3) valid is that the bounce time remains (much) smaller ⇠ ⇠ ⇠ ⇤ than the Hawking time. This assumptionII. SINGLE is supported EVENT DETECTION (Other more exotic models,wheree.g.g collisions100 is the of number cosmic of degrees of freedom. by the “firewall argument” presented in [1]. We study in ⇤ ⇠ strings or collisions of bubblesOnce associatedk is fixed, M with is fixed di↵ (byerent⌧ tH ) and T is therefore detail the maximal distance at which a single black-hole Quantum Gravity Phenomenology ⇠ Francesca Vidotto For detection purposes, wevacua, are interested can lead in to black di↵erentknown. masses at As a the given process cosmic is time. time-symmetric, what comes bounce can be detected. Second,holes we whose go beyond lifetime this is “sin- less than the age of the Universe. out from the white hole should be what went in the We will not consider them in this study.) The cosmic gle event detection” and considerFor the a primordial di↵use background black hole detected today, ⌧ = t black hole, re-emerging at the same energy: a blackbody time t is related to theH temperature of the Universe T by produced by a distribution of bouncingwhere tH is black the Hubble holes. time. This fixes the mass M, as spectrum at temperature T . Intuitively, the bouncing a function of the parameter k (defined in the previous black1 hole plays the role of a “time machine” that sends 2 2 section) for black holes that can be observed. Int all 0.3theg primordialT , universe radiation(3) to the future: while the ⇤ cases considered, M is very small compared to a solar⇠ surrounding space has cooled to 2.3K, the high-energy II. SINGLE EVENTmass DETECTION and therefore only primordialwhere blackg holes100 possibly is the numberradiation of emerges degrees from of freedom. the white hole with its original ⇤ ⇠ formed in the early Universe areOnce interestingk is fixed, from M is this fixed (byenergy.⌧ tH ) and T is therefore For detection purposes, wepoint are of interested view. Although in black no primordialknown. blackAs the hole process has is time-symmetric,⇠ what comes holes whose lifetime is less thanbeen the detected age of the to date, Universe. various mechanismout from for the their white pro- hole shouldWhen be the what parameter wentk inis taken the larger that its smallest For a primordial black holeduction detected shortly today, after⌧ the= t BigH Bangblack have hole, been re-emerging suggested atpossible the same value, energy: that a blackbodyis fixed for quantum e↵ects to be (see, e.g., [12] for an early detailed calculation and [13] important enough to lead to a bounce, the bounce time where tH is the Hubble time. This fixes the mass M, as spectrum at temperature T . Intuitively, the bouncing a function of the parameter kfor(defined a review). in the Although previous their numberblack hole density plays might the be role ofbecomes a “time larger machine” for a thatgiven sends mass. If this time is assumed way too small for direct detection, the production of to be equal to the Hubble time (or slightly less if we section) for black holes that can be observed. In all the primordial universe radiation to the future: while the primordial black holes remains a quite generic prediction focus on black holes bouncing far away), this means cases considered, M is very smallof cosmological compared to physics a solar eithersurrounding directly from space density has cooledthat to the 2.3K, mass thehas to high-energy be smaller. The resulting energy mass and therefore only primordialperturbations black holes –possibly possibly enhancedradiation by phase emerges transitions– from thewill white be higher hole with for both its original the low energy and the high formed in the early Universeor are through interesting exotic from phenomena this likeenergy. collisions of cosmic energy signals, but for di↵erent reasons. In the first point of view. Although no primordialstrings or bubbles black of hole false has vacua. case, because of the smaller size of the hole, leading been detected to date, various mechanism for their pro- When the parameter k isto taken a smaller larger emitted that its wavelength. smallest In the second case, duction shortly after the Big Bang have been suggested possible value, that is fixed for quantum e↵ects to be (see, e.g., [12] for an early detailed calculation and [13] important enough to lead to a bounce, the bounce time 2 for a review). Although their number density might be becomes larger for a given mass. If this time is assumed way too small for direct detection, the production of to be equal to the Hubble time (or slightly less if we primordial black holes remains a quite generic prediction focus on black holes bouncing far away), this means of cosmological physics either directly from density that the mass has to be smaller. The resulting energy perturbations –possibly enhanced by phase transitions– will be higher for both the low energy and the high or through exotic phenomena like collisions of cosmic energy signals, but for di↵erent reasons. In the first strings or bubbles of false vacua. case, because of the smaller size of the hole, leading to a smaller emitted wavelength. In the second case, 2 THE SMOKING GUN: DISTANCE/ENERGY4 RELATION by 1 1/2 other other 2Gm H0 1 ⌦⇤ 3/2 obs =(1+z) emitted. obs(6) 2 (1 + z) 1/2 sinh (z + 1) ⟶ ⇠ c v ⌦M u6 k⌦⇤ " # u ✓ ◆ The specific redshift dependence of our model makes t 2 it possibly testable against other proposals. Obvi- ously, detecting such a signal from far away galaxies is challenging but this work might precisely motivate some experimental prospects for the next generation ofl gamma-ray satellites. distance ∝ 1/wave length noise. There might be room for improvement. It is not The order of magnitude of the number of bouncing impossible that the time structure of the bounce could black holes in the galactic center region required to ac- count for the observed taking flux into is 100 account per second. the The asso- lead to a characteristic time-scale of the event larger than ciated mass is negligibleredshift when the compared resulting to function the expected dark matter density, even when integrated over a long the response time of the bolometer. In that case, a time interval. If theis very mass slowly spectrum varying of primordial black FIG. 3. Best fit to the Fermi excess with bouncing black holes was known, which is not the case, it would in prin- specific analysis should allow for a dedicated search of holes. ciple be possible to fix the total mass associated with bouncing black holes. As a reasonable toy model, let us such events. We leave this study for a future work as assume that the mass spectrum is given by Barrau, Rovelli, Vidotto 1409.4031 z it requires astrophysical considerations beyond this first DISCRIMINATION WITH DARK MATTER AND 2 2 4 6 8 10 d N ↵ MASS SPECTRUM = pM . (7) dMdV investigation. An isotropic angular distribution of the Quantum Gravity Phenomenology Francesca Vidotto The model presented in this work is unquestionably If the number of exploding black holes required to explain bursts, signifying their cosmological origin, could also be quite exotic when compared to astrophysical hypotheses. the data on a time intervalFIG.d⌧ is Nexp 1:, one White can estimate hole signal wavelength (unspecified units) as But the important point is than it can, in principle, be the mass variation associated, considered as an evidence for the model. In case many distinguished both from astrophysical explanations and a function of z. Notice the characteristic flattening at large d⌧ from other “beyond the standard model” scenarios. The dM = . (8) events were measured, it would be important to ensure distance:8kM the youth of the hole compensate for the redshift. reason for that is the redshift dependance. When look- ing at a galaxy at redshift z, the measured energy of With M0 the mass corresponding to a black hole explod- that there is no correlation with the mean cosmic-ray flux the signal emitted either by decaying WIMPS or by as- ing now, one then has trophysical objects will be E/(1 + z) if the rest-frame (varying with the solar activity) at the satellite location. M0+dM energy is E. But this is not true for the bouncing black ↵ Nexp = pM dM. (9) holes signal. The reason for this is that black holes that M The received signal is going to be corrected by standard Let us turn to something that has been observed. 0 have bounced far away and are observed now must have Z a smaller bouncing time and therefore a smaller mass. This allows, in principe, tocosmological determine p and therefore redshift. to However, signals coming form far- Fast Radio Bursts. Fast Radio Bursts are intense iso- Their emission energy – in the low energy channel we are normalize the spectrum. considering in this article – is therefore higher and this ther away were originated earlier, namely by younger, lated astrophysical radio signals with milliseconds dura- partly compensates for the redshift e↵ect. Following [9], we can write down the observed wavelength of the signal CONCLUSIONand therefore less massive, holes, giving a peculiar de- tion. A small number of these were initially detected from a host galaxy at redshift z, taking into account both the expansion of the universe and the change of bouncing Black holes could bouncecrease once they have of reached the the emitted wavelength with distance. The re- only at the Parkes radio telescope [39–41]. Observations time, as: “Planck star” stage. This is a well motivated quantum gravity idea. In this article,ceived we have shown wavelength, that this taking into account both the expan- from the Arecibo Observatory have confirmed the detec- 2Gm phenomenon could explain the GeV excess measured by BH (1 + z) (5) obs ⇠ c2 ⇥ the Fermi satellite. This wouldsion open of the fascinating the universe pos- and the change of time available for tion [42]. The frequency of these signals around 1.3 GHz, 1 1/2 sibility to observe (non perturbative) quantum gravity H0 1 ⌦⇤ 3/2 processes at energies 19 ordersthe of black magnitude hole below the to bounce, can be obtained folding (1)into 1/2 sinh (z + 1) , namely a wavelength v ⌦M u6 k⌦⇤ " # Planck scale. Interestingly the explanation we suggest is u ✓ ◆ t fully self consistant in the sensethe that standard the hadronic “noise” cosmological relation between redshift and where we have reinserted the Newton constant G and due to decaying pions remainsproper much below time. the observed A straightforward calculation gives the speed of light c; H0, ⌦⇤ and ⌦M being the Hubble background. Unquestionably, there are other – less exotic observed 20 cm. (7) constant, the cosmological constant, and the matter den- – ways to explain the Fermi excess. But the important sity. On the other hand, for other signals the measured point we have made is that there is specific redshift de- ⇠ wavelength this just related to the observed wavelength pendance of this model which, in principle, can2 leadGm to a obs (1 + z) (6) These signals are believed to be of extragalactic origin, ⇠ c2 ⇥ because the observed delay of the signal arrival time with 1 1/2 H0 1 ⌦⇤ frequency agrees well with the dispersion due to ionized sinh (z + 1) 3/2 . 1/2 medium as expected from a distant source. The total v ⌦M u6 k⌦⇤ " # u ✓ ◆ energy emitted in the radio is estimated to be of the t 38 where we have reinserted the Newton constant G and order 10 erg. The progenitors and physical nature of the Fast Radio Bursts are currently unknown [42]. the speed of light c while H0, ⌦⇤ and ⌦M are the Hub- ble constant, the cosmological constant, and the matter There are three orders of magnitude between the pre- density. This is a very slowly varying function of the dicted signal (5) and the observed signal (7). But the redshift. The e↵ect of the hole’s age almost compesates black-to-white hole transition model is still very rough. It for the red-shift. The signal, indeed, varies by less than disregards rotation, dissipative phenomena, anisotropies, an order of magnitude for redshifts up to the decoupling and other phenomena, and these could account for the time (z=1100). See Figure 1. discrepancy. If the redshift of the source can be estimated by using In particular, astrophysical black holes rotate: one may dispersion measures or by identifying a host galaxy, given expect the centrifugal force to lower the attraction and su cient statistics this flattening represents a decisive bring the lifetime of the hole down. This should allow signature of the phenomenon we are describing. larger black holes to explode today, and signals of larger Do we have experiments searching for these signals? wavelength. Also, we have not taken the astrophysics of There are detectors operating at such wavelengths, begin- the explosion into account. The total energy (3) avail- ning by the recently launched Herschel instrument. The able in the black hole is largely su cient –9 orders of 200 micron range can be observed both by PACS (two magnitude larger– than the total energy emitted in the bolometer arrays and two Ge:Ga photoconductor arrays) radio estimated by the astronomers. and SPIRE (a camera associated with a low to medium Given these uncertainties, the hypothesis that Fast Ra- resolution spectrometer). The predicted signal falls in be- dio Burst could originate from exploding white holes is tween PACS and SPIRE sensitivity zones. There is also a tempting and deserves to be explored. very high resolution heterodyne spectrometer, HIFI, on- High energy signal. When a black hole radiates by board Herschel, but this is not an imaging instrument, it the Hawking mechanism, its Schwarzschild radius is the observes a single pixel on the sky at a time. However, the only scale in the problem and the emitted radiation has bolometer technology makes detecting short white-hole a typical wavelength of this size. In the model we are bursts di cult. Cosmic rays cross the detectors very of- considering, the emitted particles do not come from the ten and induce glitches that are removed from the data. coupling of the event horizon with the vacuum quan- Were physical IR bursts due to bouncing black hole regis- tum fluctuations, but rather from the time-reversal of tered by the instrument, they would most probably have the phenomenon that formed (and filled) the black hole. been flagged and deleted, mimicking a mere cosmic ray Therefore the emitted signal is characterized by second 1 1 1 4 1 4 1 1 2 2 meas 2⇡ (1 +measz) H2⇡0 (1 + z)1 ⌦H⇤0 1 3⌦⇤ 3 sinh (1 + z) 2 . 2 (6) high high1 1 1/2 1 1 1/2 sinh (1 + z) . (6) ⇠ kBT (0.3g ) 2 ⇠"6kkB⌦T (0.3g ) 2""6⌦kM⌦ " ⌦##M ## ⇤ ⇤ ⇤ ✓ ⇤◆ ✓ ◆ This shows that althoughThis shows the that mean although wavelength the mean does wavelengthIt is worth does consideringIt is worth the consideringn(R) term the a bitn(R more) term in a bit more in dn dn decreases as a functiondecreases of k asin a both function cases, of itk doesin both not cases,detail. it does If not one denotesdetail. by If one denotesthe initial by dMdV di↵erentialthe initial di↵erential 1 1 dMdV follow the same general behavior. It2 scales with k 2 mass spectrum of primordial black holes per unit volume, follow the same general behavior. It scales with k 1mass spectrum of primordial black holes per unit volume, for the low energy component1 and as k 4 for the high it is possible to define n(R) as: for the low energy component and as k 4 for the high it is possible to define n(R) as: energy one. energy one. M(t+ t) M(t+ t) dn dn The following conclusions can be drawn: n(R)= n(R)= dM, (8)dM, (8) The following conclusions can be drawn: dMdVM(t) dMdV ZM(t) Z The low energy channelThe low leads energy to achannel better leads single- to a better single- • event detection than the high energy channel. leading to • event detection than the high energy channel. leading to Although lower energy dilutes the signal in a Although lower energy dilutes the signal in a dn t higher astrophysical background, this e↵ect is over- dn n(tR) , (9) higher astrophysicalcompensated background, by this the e↵ largerect is amount over- of photons. n(R) , ⇡ dMdV 8k (9) compensated by the larger amount of photons. ⇡ dMdV 8k The di↵erence of maximal distances between the where the mass spectrum is evaluated for the mass cor- The di↵erence of• maximallow- and high distances energy betweenchannels the decreaseswhere for the higher mass spectrumresponding is to evaluated a time (t for theR ). mass If one cor- assumes that pri- • INTEGRATED EMISSION R H c low- and high energyvalueschannels of k, i.e. decreases for longer for higherblack-holeresponding lifetimes. to a time (tH c ). If one assumes that pri- Barrau, Bolliet,mordial Vidotto, black Weimer holes 1507.1198 are directly formed by the collapse values of k, i.e. for longer black-hole lifetimes. mordial black holesof density are directly fluctuations formed with by a the high-enough collapse density con- In the low energy channel,⌧ form the2 smaller values • ⇠ of density fluctuationstrast in with the early a high-enough Universe, the density initial con- mass spectrum is In the low energy channel,of k, a single for thebounce smaller can be values detectedtrast arbitrary in the far early Universe, the initial mass spectrum is • of k, a single bounce can be detected arbitrary far directly related to the equation of state of the Universe Low energyaway channel in the Universe. directlyHigh energy related channel toat the the equationformation of epoch. state It of is the given Universe by [18, 19]: away in the Universe. k=0.05 In all cases, the distances are large enoughat the and formation ex-direct epoch. It is given bydecayed [18, 19]: In all cases, the distances• are large enough and ex- dn 1 1+3w perimental detection is far from being hopeless. = ↵M 1+w , (10) • k=0.05 k=100 dn 1dMdV1+3w perimental detection is far from being hopeless. = ↵M 1+w , (10) dMdV III. INTEGRATED EMISSION where w = p/⇢. In a matter-dominated universe the 1+3w III. INTEGRATED EMISSION where w = p/⇢.exponent In a matter-dominated 1 1+w takes universe the the value = 5/2. direct+decayed The normalization1+3w ⌘ enlarged coe cient ↵ will be kept unknown In addition to the instantaneous spectrumexponent emitted by a 1 1+w takes the value = 5/2. ⌘ as it depends on the details of the black hole formation single bouncing black hole, it is interesting toThe consider normalization the coe cient ↵ will be kept unknown In addition to the instantaneous spectrum emitted by a mechanism. For a sizeable amount of primordial black k=10000 as it dependsk=109 on the details of the black hole formation single bouncing blackpossible hole, it di is↵use interesting background to consider due to the the integrated emis- mechanism. Forholes a sizeable to form, amount the power of primordial spectrum black normalized on the possible di↵use backgroundsion of a populationdue to the of integrated bouncing emis- black holes. Formally, holes to form, theCMB power needs spectrum to be boosted normalized at small on the scales. This can sion of a populationthe of number bouncing of measured black holes. photons Formally, detected per unit time, CMB needs to bebe achieved,boosted at for small example, scales. through This Staobinsky’s can broken the number of measuredunit energy photons and detected unit surface, per unit can time, be written as: be achieved, forscale example, invariance through (BSI) Staobinsky’s scenario. broken The idea is that the unit energy and unit surface, can be written as: dNmes scale invariancemass (BSI) spectrum scenario. takes The a high idea enough is that value the in the relevant = ind((1+z)E,R) n(R) Acc Abs(E,Rcharacteristic)dR, shape: distorted black body dN dEdtdS · · · mass spectrum takesrange a whereas high enough it is naturally value in the suppressed relevant at small masses mes Z by inflation and at large masses by the BSI hypothesis. = ind((1+z)E,R) n(R) Acc Abs(E,R)dR, range whereas(7) it is naturally suppressed at small masses dEdtdS where (·E,R)· denotes· the individual flux emitteddepends on howWe much will not DM study are PBL those questions here and just consider Z ind (7) by inflation and at large masses by the BSI hypothesis. by a single bouncing black hole at distance R and at the shape of the resulting emission, nor its normalisation We will not study those questions here and just consider where ind(E,R) denotesenergy E the, Acc individualis the angular flux acceptance emitted of the detector which depends sensitively on the bounds of the mass Quantum Gravity Phenomenology the shape of the resulting emission,Francesca Vidotto nor its normalisation by a single bouncingmultiplied black hole by its at e distance ciencyR (inand principle at this is also a spectrum, that are highly model-dependent. As this part energy E, Acc is thefunction angular of acceptanceE but this of will the be detector ignored here),whichAbs( dependsE,R) sensitivelyof the study on is thedevoted bounds to the of investigation the mass of the shape multiplied by its eis ciency the absorption (in principle function, this and is alson(R) a is thespectrum, number that of areof highlythe signal, model-dependent. the y axis on the As figures this part are not normalized. function of E but thisblack will holes be bouncingignored here), at distanceAbs(E,RR per) unitof the time study and is devoted to the investigation of the shape is the absorption function,volume. and Then distance(R) is theR numberand the of redshiftof thez entering signal, the y axisFortunately, on the figures the results are not are normalized. weakly dependent upon black holes bouncingthe at above distance formulaR per are unit linked. time The and integration has to the shape of the mass spectrum. This is illustrated in volume. The distancebe carriedR and out the up redshift to cosmologicalz entering distancesFortunately, and it is theFig. results 5 where are di↵ weaklyerent hypothesis dependent for upon the exponent are the above formulatherefore are linked. necessary The integration to use exact has results to behindthe the shape linear of thedisplayed. mass spectrum. The resulting This is electromagnetic illustrated in spectrum is be carried out upapproximation. to cosmological The distances energy and is also it is correlatedFig. 5 with whereR di↵erentalmost hypothesis exactly the for same. the exponent Therefore are we only keep one therefore necessaryas to theuse exactdistance results fixes behind the bounce the linear time of thedisplayed. black hole Thecase resulting ( = electromagnetic5/2, corresponding spectrum to w =1 is/3). The black approximation. Thewhich, energy subsequently, is also correlated fixes the emitted with R energy.almost exactly theholes same. are assumed Therefore to we be only uniformly keep onedistributed in the as the distance fixes the bounce time of the black hole case ( = 5/2,Universe, corresponding which to isw a=1 meaningful/3). The hypothesis black as long as which, subsequently, fixes the emitted energy. holes are assumed to be uniformly distributed in the Universe, which is a meaningful hypothesis as long as 5 5 1 1 4 1 2 meas 2⇡ (1 + z) H0 1 ⌦⇤ 3 2 high 1 1 1/2 sinh (1 + z) . (6) ⇠ kBT (0.3g ) 2 "6k⌦ " ⌦M ## ⇤ ⇤ ✓ ◆ This shows that although the mean wavelength does It is worth considering the n(R) term a bit more in decreases as a function of k in both cases, it does not detail. If one denotes by dn the initial di↵erential 1 dMdV follow the same general behavior. It scales with k 2 mass spectrum of primordial black holes per unit volume, 1 for the low energy component and as k 4 for the high it is possible to define n(R) as: energy one. 1 M(t+ t) 1 4 dn 1 2 meas 2⇡ (1 + z) H0 1 ⌦⇤ 3 n(R)= dM, (8) The following conclusions can be drawn: 2 high 1 1 1/2 sinh (1 + z) . M((6)t) dMdV ⇠ kBT (0.3g ) 2 "6k⌦ " ⌦M ## Z The low energy⇤ channel⇤ leads to✓ a better◆ single- • event detection than the high energy channel. leading to Although lower energy dilutes the signal in a 1 1 4 dn t 1 higher astrophysical2 background, this e↵ect is over- meas This2⇡ shows(1 + thatz) althoughH0 the1 mean⌦ wavelength⇤ does3 It is worth considering the n(R) term a bitn more(R) in , (9) 2 dMdV 8k high 1 1 1/2 sinh compensated(1 by + z the) larger. amount of photons. (6) dn ⇡ decreases⇠ kBT (0 as.3g a function) 2 of k in both⌦ cases,M it does not detail. If one denotes by dMdV the initial di↵erential "6k⌦⇤ "✓ ◆ 1## follow the same⇤ general behavior. It scales with k 2 mass spectrum of primordial black holes per unit volume, The di↵erence1 of maximal distances between the where the mass spectrum is evaluated for the mass cor- for the low energy component• and as k 4 for the high it is possible to define n(R) as: R low- and high energy channels decreases for higher responding to a time (tH c ). If one assumes that pri- energy one. values of k, i.e. for longer black-hole lifetimes. mordial black holes are directly formed by the collapse This shows that although the mean wavelength does It is worth considering the n(R) term a bit more inM(t+ t) dn n(R)= of densitydM, fluctuations with(8) a high-enough density con- decreases as a function of k in bothThe following cases, it does conclusions not candetail. beIn drawn: the If onelowPBH denotes energy MASSchannel, by SPECTRUMdn forthe the initial smaller di↵erential values trastdMdV in the early Universe, the initial mass spectrum is 1 • of k, a singlePBH bounce MASS candMdV SPECTRUM be detected arbitraryZ farM(t) follow the same general behavior. It scales with k 2 mass spectrum of primordial black holes per unit volume, directly related to the equation of state of the Universe The low1 energy channel leadsaway to in a the better Universe. single- for the low energy component and• aseventk 4 detectionfor the high thanit the is possiblehigh energy to definechannel.n(R) as:leading to at the formation epoch. It is given by [18, 19]: energy one. Although lower energy dilutes the signal in a In all cases, the distancesM(t+ t are) large enough and ex- higher astrophysical background,• this e↵ect is over- dn dn t dn 1 1+3w perimentaln( detectionR)= is far from beingdM, hopeless.n(R(8)) , =(9)↵M 1+w , (10) The following conclusions can be drawn:compensated by the larger amount of photons. dMdV ⇡ dMdV 8k dMdV ZM(t) The low energy channel leads to a better single- The di↵erence of maximal distances between the where the mass spectrum is evaluated for the mass cor- • event detection than the high energy channel. leading toIII. INTEGRATED EMISSION where w = p/⇢. In a matter-dominated universe the • low- and high energy channels decreasesLow for energy higher channelresponding to a time (t R ). If one assumes that1+3 pri-w Although lower energy dilutes the signal in a H exponentc 1 1+w takes the value = 5/2. values of k, i.e. for longer black-hole lifetimes. mordial black holes are directly formed by⌘ the collapse higher astrophysical background, this e↵ect is over- dn t The normalization coe cient ↵ will be kept unknown In addition to the instantaneousn(R) of spectrum density, fluctuations emitted by(9) a with a high-enough density con- compensated by the larger amount of photons.1 ⇡ dMdV 8k as it depends on the details of the black hole formation behavior. It scalesIn the withlowk 2 energyfor thechannel, lowsingle energy bouncing for compo- the smaller black hole, values it is interesting to consider the • 1 trast in the early Universe, themechanism. initial mass For spectrum a sizeable is amount of primordial black nent and as k of4 fork, a the single high bounce energy one.The canpossible be detected following di↵use backgroundarbitrary far due to the integrated emis- The di↵erence of maximal distances between the where the mass spectrum is evaluateddirectly for related the mass to the cor- equationholes of to state form, of theDifferent the Universe power mass spectrum spectra normalized on the • conclusions canaway be drawn: in the Universe.sion of a population of bouncingR black holes. Formally, low- and high energy channels decreases for higher responding to a time (tH ).at If the one formation assumes that epoch. pri- It isCMB given needs by [18, to 19]:gives be boosted qualitatively at small same scales. This can the number of measured photons c detected per unit time, values of k, i.e. for longerThe black-holelow energyIn all cases, lifetimes.channel the leads distances to amordial better are large single- black enough holes and are ex- directly formed by the collapse be achieved, for example,diffuse emission… through Staobinsky’s broken • • unit energy and unit surface, can be written as: 1+3w event detectionperimental than the detectionhigh energy isof farchannel. density from being fluctuations Al- hopeless. with a high-enough densitydn con- scale1 invariance (BSI) scenario. The idea is that the In the low energy channel, for the smaller values = ↵M 1+w , (10) • though a lower energy dilutes thedNtrastmes signal in the in early a Universe, the initial mass spectrumdMdV is mass spectrum takes a high enough value in the relevant of k, a single bounce can be detected arbitrary far = ((1+z)E,R) n(R) Acc Abs(E,R)dR, higher astrophysical background, thisdEdtdSdirectly e↵ect is related over-ind to the equation of state of the Universe range whereas it is naturally suppressed at small masses away in the Universe. · where· w ·= p/⇢. In a matter-dominated universe the compensated byIII. the larger INTEGRATED amountat of thephotons. EMISSION formationZ epoch. It is given by [18, 19]: (7) by inflation and at large masses by the BSI hypothesis. exponent 1 1+3w takes the value = 5/2. In all cases, the distancesThe are di↵erence large enough of maximal and ex- distanceswhere between ind(E,R the ) denotes the individual flux⌘ emitted 1+w We will not study those questions here and just consider • dn The1+3 normalizationw coe cient ↵ will be kept unknown perimental detection• is far fromIn addition being hopeless. to the instantaneousby a single spectrum bouncing emitted black by a hole1 at1+ distancew R and at the shape of the resulting emission, nor its normalisation low- and high energy channels decreases for higher = ↵M as it depends, on the(10) details of the black hole formation valuessingle of k bouncing, i.e. for longer black black-holehole, itenergy is interesting lifetimes.E, Acc tois consider thedMdV angular the acceptance of the detector which depends sensitively on the bounds of the mass mechanism. For a sizeable amount of primordial black possible di↵use backgroundmultiplied due to the by integrated its e ciency emis- (in principle this is also a spectrum, that are highly model-dependent. As this part where w = p/⇢. In a matter-dominatedholes to form, universe the power the spectrum normalized on the III. INTEGRATEDIn thesion EMISSIONlow of energy a populationchannel, of for bouncing thefunction smaller black of valuesE holes.but this Formally, will be ignored here), Abs(E,R) of the study is devoted to the investigation of the shape • of k, a single bounce can be detectedexponent arbitrary far 1 1+3w takesCMB the needs value to = be boosted5/2. at small scales. This can the number of measured photonsis the detected absorption per function, unit time,1+w and n(R) is the number of of the signal, the y axis on the figures are not normalized. away in the Universe. The normalization⌘ coe cient ↵bewill achieved, be kept for unknown example, through Staobinsky’s broken In addition to the instantaneousunit spectrum energy and emitted unit by surface, a black can holes be written bouncingQuantum as:FIG. atGravity 5: distance LowPhenomenology energyR perchannel unit signal time calculated and for di↵erent Francesca Vidotto as it depends on themass details spectra. ofscale As the the black invariance mass hole spectrum formation (BSI) is not scenario. normalized, The the idea is that the single bouncing black hole, it is interesting to consider the volume. The distance R and the redshift z entering Fortunately, the results are weakly dependent upon In alldN cases, the distances are largemechanism. enough and ex- For aunits sizeable of the amounty axismass are spectrum of arbitrary. primordial takes black a high enough value in the relevant possible di↵use background• perimental due tomes the detection integrated is far emis- from beingthe above hopeless. formula are linked. The integration has to the shape of the mass spectrum. This is illustrated in = ind((1+z)E,Rholes) n(R to) Acc form,Abs the(E,R power)dR, spectrumrange whereas normalized it is on naturally the suppressed at small masses sion of a population of bouncingdEdtdS black holes. Formally, be carried· · out· up to cosmological distances and it is Fig. 5 where di↵erent hypothesis for the exponent are Z CMB needs to be boosted(7) atby small inflation scales. and This at large can masses by the BSI hypothesis. the number of measured photons detected per unit time, therefore necessary towhere use the exact mass results spectrum behind is evaluated the linear for thedisplayed. mass cor- The resulting electromagnetic spectrum is whereIII. INTEGRATED ind(E,R) denotes EMISSION thebe individual achieved, for flux example, emitted throughWe will Staobinsky’s not studyR thosebroken questions here and just consider unit energy and unit surface, can be written as: approximation. Theresponding energy is to also a time correlated (tH ). with TheR shapealmost of the mass exactly the same. Therefore we only keep one by a single bouncing black holescale at invariance distance (BSI)R and scenario. at the The shape idea of the isc resulting that the emission, nor its normalisation as the distance fixesspectrum the bounce obviously time depends of the black on the hole detailscase of the ( for-= 5/2, corresponding to w =1/3). The black dNmes In additionenergy to theE, instantaneousAcc is the angular spectrummass acceptance emitted spectrum by of a the takesmation detector a high mechanism enoughwhich value (see depends [39] in the for sensitively relevant a review on on PBHs the bounds and of the mass = ind((1+z)E,R) n(R) Acc Abs(E,R)dR, which, subsequently, fixes the emitted energy. holes are assumed to be uniformly distributed in the dEdtdS single bouncingmultiplied· black· · hole,by its it is e interestingciency (inrange to considerprinciple whereas the this it is isinflation). naturally also a As suppressedspectrum, an example, at that we small are shall masses highly assume model-dependent. that primor- As this part Z Universe, which is a meaningful hypothesis as long as possible difunction↵use background of E but due this to(7) will the be integratedby ignored inflation emis- here), andAbs atdial large(E,R black masses) holesof by the are the study directly BSI is hypothesis. formed devoted by to the the collapse investigation of of the shape where ind(E,R) denotession of the ais population individual the absorption of flux bouncing emitted function, black and holes.Wen will( Formally,R) not is studythe numberdensity those questions of fluctuationsof the here with signal, and a high-enoughjust the y consideraxis on density the figures contrast are not normalized. by a single bouncingthe black number holeblack of at measured holesdistance bouncing photonsR and detected at at distancethe per shape unitR per time, of unit the resulting timein the and early emission, Universe. nor The its normalisation initial mass spectrum5 is then energy E, Acc is the angularunit energy acceptancevolume. and unit The of surface, the distance detector can beR writtenandwhich the as: depends redshift sensitivelyz directlyentering related on the toFortunately, bounds the equation of the the of state results mass of arethe Universe weakly dependent upon multiplied by its e ciency (inthe principle above formula this is also are linked.a spectrum, The integration that areat highly has the formation to model-dependent.the epoch. shape It of is As the given this mass by part [33, spectrum. 40]: This is illustrated in dNmes function of E but this will be=be ignored carried ind here),((1+ outz)AbsE,R up()E,R ton( cosmologicalR)) A(ofE) thef(E,R study distances)dR, is devoted and it to is the investigationFig. 5 where of di↵ theerent shape hypothesis for the exponent are dEdtdS · · · dn 1 1+3w is the absorption function, andthereforen(R) is necessary the number to use of exactof the results signal, behind the y theaxis linear on the figuresdisplayed. are not= ↵ TheM normalized. resulting 1+w , electromagnetic(14) spectrum is Z (11) dMdV black holes bouncing at distanceapproximation.R per unit time The and energy is also correlated with R almost exactly the same. Therefore we only keep one where ind(E,R) denotes the individual flux emitted volume. The distancebyR aand singleas the bouncingthe redshift distance blackz fixesentering hole the at bounce distanceFortunately, timeR and of at the the blackwhere results holew = arep/case weakly⇢. In( a= dependent matter-dominated5/2, corresponding upon universe to w the=1/3). The black the above formula are linked.which, The integration subsequently, has fixes to thethe emitted shape energy. of the massexponent spectrum. holes1 This are1+3 is assumed w illustratedtakes the to value bein uniformly = 5/2. distributed in the energy E, A(E) is the angular acceptance of the detector ⌘ 1+w be carried out up tomultiplied cosmological by its distances e ciency, andf(E,R it is) isFig. the absorption 5 where di↵erentThe hypothesis normalizationUniverse, for coe the exponent whichcient ↵ iswill a meaningfulare be kept unknown hypothesis as long as therefore necessary to usefunction, exact and resultsn(R) behind is the number the linear of blackdisplayed. holes bouncing The resultingas it depends electromagnetic on the details spectrum of the black is hole formation approximation. Theat energy distance is alsoR per correlated unit time with and volume.R almost The distance exactly themechanism. same. Therefore For a sizeable we only amount keep of one primordial black as the distance fixes theR and bounce the time redshift of thez entering black hole the abovecase formula ( = are5/2, correspondingholes to form,5 to thew power=1/3). spectrum The black normalized on the which, subsequently, fixeslinked. the emitted The integration energy. has to be carriedholes out are up assumed to CMB to be needs uniformly to be boosted distributed at small in scales. the The formula cosmological distances and it is thereforeUniverse, necessary which to isgiven a meaningful above might hypothesis therefore as be long correct as only within a use exact results behind the linear approximation. The limited interval of masses. The idea is that the mass energy is also correlated with R as the distance fixes the spectrum takes a high enough value in the relevant bounce time of the black hole which, subsequently,5 fixes range whereas it is naturally suppressed at small masses the emitted energy. by inflation. We will neither study those questions here (focusing on the shape of the resulting emission), It is worth considering the n(R) term a bit more into nor the normalisation issues which depend sensitively dn on the bounds of the mass spectrum, that are highly the details. If one denotes by dMdV the initial di↵erential mass spectrum of primordial black holes per unit volume, model-dependent. As this part of the study is devoted it is possible to define n(R) as: to the investigation of the shape of the signal, the y axis on the figures are not normalized. As we show M(t+ t) dn below, the shape of the signal is quite independent on n(R)= dM, (12) the shape of the mass spectrum, so Eq. 14 does not play dMdV ZM(t) any significant role for the spectra computer. leading to The results are indeed very weakly dependent upon dn t the shape of the mass spectrum. This is illustrated in n(R) , (13) ⇡ dMdV 8k Fig. 5 where di↵erent hypothesis for the exponent are 6 SUMMARY ON REMNANTS 1. BOUNCE2 : Bouncing BH in a Bouncing Universe - Planckian remnants pass trough the bounce and are viable dark matter - large “old” volume inside remnants make up all the volume of the universe * solve the problem with the Past Hypothesis in a perspectival manner 2. REMNANTS AS DARK MATTER * compatible with PBH formation at reheating * STABILITY OF THE REMNANTS via minimal area/mass Quantum Gravity Phenomenology Francesca Vidotto SUMMARY 1. PHENOMENOLOGY depends mainly on the lifetime given as a function of the mass: as short as m2 * interesting to check prediction by different QG frameworks! 2. NEW EXPERIMENTAL WINDOWS for quantum gravity * new experimental window for quantum gravity signals in the sub-mm, radio & TeV direct detection & diffuse emission peculiar energy distance relation 3. PRIMORDIAL BLACK HOLES new features Also for late-universe observations Quantum Gravity Phenomenology Francesca Vidotto MAIN REFERENCES Planck Stars Planck stars Carlo Rovelli, Francesca Vidotto Int. J. Mod. Phys. D23 (2014) 12, 1442026 Cosmic Rays Planck star phenomenology Planck stars as observational probes of Aurelien Barrau, Carlo Rovelli. quantum gravity Carlo Rovelli Phys. Lett. B739 (2014) 405 Nature Astronomy, March’17, comment Fast Radio Bursts and White Hole Signals Aurélien Barrau, Carlo Rovelli, Francesca Vidotto. Phys. Rev. D90 (2014) 12, 127503 Phenomenology of bouncing black holes in quantum gravity: a closer look Aurélien Barrau, Boris Bolliet, Francesca Vidotto, Celine Weimer JCAP 1602 (2016) no.02, 022 Fast radio bursts and the stochastic lifetime of black holes in quantum gravity Aurélien Barrau, Flora Moulin, Killian Martineau Phys.Rev. D97 (2018) no.6, 066019 Late Cosmo. Quantum effects of Primordial Black Holes on Galaxy Clustering Alvise Raccanelli, Licia Verde, Francesca Vidotto Remnants White Holes as Remnants: A Surprising Scenario for the End of a Black Hole Eugenio Bianchi, Marios Christodoulou, Fabio D’Ambrosio, Hal Haggard, Carlo Rovelli e-Print: arXiv:1802.04264 Small black/white hole stability and dark matter Carlo Rovelli, Francesca Vidotto. e-Print: arXiv:1805.03872 Erebons Pre-big-bang black-hole remnants and the past low entropy Carlo Rovelli, Francesca Vidotto. e-Print: arXiv:1805.03224 Quantum Black Holes Francesca Vidotto