Black Hole Hawking Radiation is turned off by infalling matter or radiation
George Ellis
University of Cape Town
Karl Schwarzschild Meeting 2015, FIAS
Karl Schwarzschild Meeting 2015, FIAS 1 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Black hole evaporation? A semiclassical investigation
The issue of black hole evaporation is still quite undecided. The case is made here that in the case of astrophysical black holes imbedded in the expanding universe filled with cosmic background radiation, Hawking radiation is emitted in the vicinity of marginally trapped surfaces (‘MOTS’), which are locally defined, rather than the event horizon, which is globally defined. Infalling radiation or matter makes the relevant MOTS spacelike, so no Hawking radiation is emitted until very late times, if at all. The black hole then may or may not evaporate; in fact it may be that no event horizon ever forms because Hawking radiation carries mass away to infinity before this occurs. One must use a full dynamic analysis to check if this is the case: studying solutions with timelike Killing vectors is not enough. Karl Schwarzschild Meeting 2015, FIAS 2 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Classical black hole event horizon Trapping by the event horizon
Figure: Black hole ingoing and outgoing light rays.
Eddington-Finkelstein diagram of a (static) black hole. Event horizon as boundary of outgoing light rays, and also as a MOTS surface: θ+ = 0. Karl Schwarzschild Meeting 2015, FIAS 3 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Classical black hole event horizon
Figure: Formation of a black hole
Eddington-Finkelstein diagram of spherical black hole formation. The vacuum exterior is static. Event horizon is one-way surface. Karl Schwarzschild Meeting 2015, FIAS 4 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Classical black hole formation Penrose diagram
Figure: Penrose diagram of spherical collapse of a star to form a black hole
The exterior region is static and asymptotically flat. The event horizon is a MOTS. Karl Schwarzschild Meeting 2015, FIAS 5 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Virtual pairs are produced by quantum vacuum, usually recombine in short order Black hole context: they get separated by the event horizon, cannot recombine Negative energy density radiation falls in, positive goes out: so energy is conserved, black body radiation emitted Effect is to transfer mass from interior to exterior It is supposed this eventually leads to a black hole explosion (Hawking)
Hawking radiation Quantum field theory in classical curved spacetime
S W Hawking (1974). ”Black hole explosions?”. Nature 248 (5443):
Karl Schwarzschild Meeting 2015, FIAS 6 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Black hole context: they get separated by the event horizon, cannot recombine Negative energy density radiation falls in, positive goes out: so energy is conserved, black body radiation emitted Effect is to transfer mass from interior to exterior It is supposed this eventually leads to a black hole explosion (Hawking)
Hawking radiation Quantum field theory in classical curved spacetime
S W Hawking (1974). ”Black hole explosions?”. Nature 248 (5443): Virtual pairs are produced by quantum vacuum, usually recombine in short order
Karl Schwarzschild Meeting 2015, FIAS 6 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Negative energy density radiation falls in, positive goes out: so energy is conserved, black body radiation emitted Effect is to transfer mass from interior to exterior It is supposed this eventually leads to a black hole explosion (Hawking)
Hawking radiation Quantum field theory in classical curved spacetime
S W Hawking (1974). ”Black hole explosions?”. Nature 248 (5443): Virtual pairs are produced by quantum vacuum, usually recombine in short order Black hole context: they get separated by the event horizon, cannot recombine
Karl Schwarzschild Meeting 2015, FIAS 6 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 so energy is conserved, black body radiation emitted Effect is to transfer mass from interior to exterior It is supposed this eventually leads to a black hole explosion (Hawking)
Hawking radiation Quantum field theory in classical curved spacetime
S W Hawking (1974). ”Black hole explosions?”. Nature 248 (5443): Virtual pairs are produced by quantum vacuum, usually recombine in short order Black hole context: they get separated by the event horizon, cannot recombine Negative energy density radiation falls in, positive goes out:
Karl Schwarzschild Meeting 2015, FIAS 6 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Effect is to transfer mass from interior to exterior It is supposed this eventually leads to a black hole explosion (Hawking)
Hawking radiation Quantum field theory in classical curved spacetime
S W Hawking (1974). ”Black hole explosions?”. Nature 248 (5443): Virtual pairs are produced by quantum vacuum, usually recombine in short order Black hole context: they get separated by the event horizon, cannot recombine Negative energy density radiation falls in, positive goes out: so energy is conserved, black body radiation emitted
Karl Schwarzschild Meeting 2015, FIAS 6 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 It is supposed this eventually leads to a black hole explosion (Hawking)
Hawking radiation Quantum field theory in classical curved spacetime
S W Hawking (1974). ”Black hole explosions?”. Nature 248 (5443): Virtual pairs are produced by quantum vacuum, usually recombine in short order Black hole context: they get separated by the event horizon, cannot recombine Negative energy density radiation falls in, positive goes out: so energy is conserved, black body radiation emitted Effect is to transfer mass from interior to exterior
Karl Schwarzschild Meeting 2015, FIAS 6 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Hawking radiation Quantum field theory in classical curved spacetime
S W Hawking (1974). ”Black hole explosions?”. Nature 248 (5443): Virtual pairs are produced by quantum vacuum, usually recombine in short order Black hole context: they get separated by the event horizon, cannot recombine Negative energy density radiation falls in, positive goes out: so energy is conserved, black body radiation emitted Effect is to transfer mass from interior to exterior It is supposed this eventually leads to a black hole explosion (Hawking)
Karl Schwarzschild Meeting 2015, FIAS 6 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Hawking radiation process Energy conservation occurs
Figure: Semi-classical Hawking radiation
Compensated ingoing and outgoing radiation is emitted Karl Schwarzschild Meeting 2015, FIAS 7 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Quantum black hole evaporation Static exterior: event horizon is MOTS
Figure: Penrose diagram of semi-classical effect of Hawking radiation
Negative energy density eats away at singularity: black hole explodes (all the radiation arrives at infinity in finite time) Karl Schwarzschild Meeting 2015, FIAS 8 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Standard view is based on applying energy conservation to singularity Negative energy reduces mass of singularity But why should singularity obey energy conservation? It’s outside of space time There are no laws for its behaviour There are no open neighbourhoods where one can define the laws that should apply Major unproven and untestable assumption. Why should we believe it? - take the singularity seriously Its the end of space, time, and physics (Wheeler) Else maybe a quantum gravity bounce to a new domain?
Problems with the standard view
This proposal is quite problematic.
Karl Schwarzschild Meeting 2015, FIAS 9 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Negative energy reduces mass of singularity But why should singularity obey energy conservation? It’s outside of space time There are no laws for its behaviour There are no open neighbourhoods where one can define the laws that should apply Major unproven and untestable assumption. Why should we believe it? - take the singularity seriously Its the end of space, time, and physics (Wheeler) Else maybe a quantum gravity bounce to a new domain?
Problems with the standard view
This proposal is quite problematic. Standard view is based on applying energy conservation to singularity
Karl Schwarzschild Meeting 2015, FIAS 9 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 But why should singularity obey energy conservation? It’s outside of space time There are no laws for its behaviour There are no open neighbourhoods where one can define the laws that should apply Major unproven and untestable assumption. Why should we believe it? - take the singularity seriously Its the end of space, time, and physics (Wheeler) Else maybe a quantum gravity bounce to a new domain?
Problems with the standard view
This proposal is quite problematic. Standard view is based on applying energy conservation to singularity Negative energy reduces mass of singularity
Karl Schwarzschild Meeting 2015, FIAS 9 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 It’s outside of space time There are no laws for its behaviour There are no open neighbourhoods where one can define the laws that should apply Major unproven and untestable assumption. Why should we believe it? - take the singularity seriously Its the end of space, time, and physics (Wheeler) Else maybe a quantum gravity bounce to a new domain?
Problems with the standard view
This proposal is quite problematic. Standard view is based on applying energy conservation to singularity Negative energy reduces mass of singularity But why should singularity obey energy conservation?
Karl Schwarzschild Meeting 2015, FIAS 9 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Major unproven and untestable assumption. Why should we believe it? - take the singularity seriously Its the end of space, time, and physics (Wheeler) Else maybe a quantum gravity bounce to a new domain?
Problems with the standard view
This proposal is quite problematic. Standard view is based on applying energy conservation to singularity Negative energy reduces mass of singularity But why should singularity obey energy conservation? It’s outside of space time There are no laws for its behaviour There are no open neighbourhoods where one can define the laws that should apply
Karl Schwarzschild Meeting 2015, FIAS 9 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Its the end of space, time, and physics (Wheeler) Else maybe a quantum gravity bounce to a new domain?
Problems with the standard view
This proposal is quite problematic. Standard view is based on applying energy conservation to singularity Negative energy reduces mass of singularity But why should singularity obey energy conservation? It’s outside of space time There are no laws for its behaviour There are no open neighbourhoods where one can define the laws that should apply Major unproven and untestable assumption. Why should we believe it? - take the singularity seriously
Karl Schwarzschild Meeting 2015, FIAS 9 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Else maybe a quantum gravity bounce to a new domain?
Problems with the standard view
This proposal is quite problematic. Standard view is based on applying energy conservation to singularity Negative energy reduces mass of singularity But why should singularity obey energy conservation? It’s outside of space time There are no laws for its behaviour There are no open neighbourhoods where one can define the laws that should apply Major unproven and untestable assumption. Why should we believe it? - take the singularity seriously Its the end of space, time, and physics (Wheeler)
Karl Schwarzschild Meeting 2015, FIAS 9 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Problems with the standard view
This proposal is quite problematic. Standard view is based on applying energy conservation to singularity Negative energy reduces mass of singularity But why should singularity obey energy conservation? It’s outside of space time There are no laws for its behaviour There are no open neighbourhoods where one can define the laws that should apply Major unproven and untestable assumption. Why should we believe it? - take the singularity seriously Its the end of space, time, and physics (Wheeler) Else maybe a quantum gravity bounce to a new domain?
Karl Schwarzschild Meeting 2015, FIAS 9 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Global: Don Page, Roger Penrose, Stephen Hawking (?), Local: Parikh and Wilczek, Matt Visser, Tim Clifton, Alex Nielsen, Paranjape and Padmanabhan, “Essential and inessential features of Hawking radiation” M Visser International Journal of Modern Physics D 12 (04), 649-661 (2003) In former case: don’t know where event horizon is: won’t be determined till end of universe e.g. Galaxy BH merge with Andromeda BH. So how does the local physics know when/where to emit radiation? Cannot be checked in the Schwarzschild solution: a degenerate case where they coincide. Then yes its given off from the event horizon, but maybe because its an apparent horizon.
The first key issue Local or global horizons?
The big issue: Is Hawking radiation determined by a global event horizon? by a local apparent horizon?
Karl Schwarzschild Meeting 2015, FIAS 10 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Local: Parikh and Wilczek, Matt Visser, Tim Clifton, Alex Nielsen, Paranjape and Padmanabhan, “Essential and inessential features of Hawking radiation” M Visser International Journal of Modern Physics D 12 (04), 649-661 (2003) In former case: don’t know where event horizon is: won’t be determined till end of universe e.g. Galaxy BH merge with Andromeda BH. So how does the local physics know when/where to emit radiation? Cannot be checked in the Schwarzschild solution: a degenerate case where they coincide. Then yes its given off from the event horizon, but maybe because its an apparent horizon.
The first key issue Local or global horizons?
The big issue: Is Hawking radiation determined by a global event horizon? by a local apparent horizon? Global: Don Page, Roger Penrose, Stephen Hawking (?),
Karl Schwarzschild Meeting 2015, FIAS 10 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 “Essential and inessential features of Hawking radiation” M Visser International Journal of Modern Physics D 12 (04), 649-661 (2003) In former case: don’t know where event horizon is: won’t be determined till end of universe e.g. Galaxy BH merge with Andromeda BH. So how does the local physics know when/where to emit radiation? Cannot be checked in the Schwarzschild solution: a degenerate case where they coincide. Then yes its given off from the event horizon, but maybe because its an apparent horizon.
The first key issue Local or global horizons?
The big issue: Is Hawking radiation determined by a global event horizon? by a local apparent horizon? Global: Don Page, Roger Penrose, Stephen Hawking (?), Local: Parikh and Wilczek, Matt Visser, Tim Clifton, Alex Nielsen, Paranjape and Padmanabhan,
Karl Schwarzschild Meeting 2015, FIAS 10 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 In former case: don’t know where event horizon is: won’t be determined till end of universe e.g. Galaxy BH merge with Andromeda BH. So how does the local physics know when/where to emit radiation? Cannot be checked in the Schwarzschild solution: a degenerate case where they coincide. Then yes its given off from the event horizon, but maybe because its an apparent horizon.
The first key issue Local or global horizons?
The big issue: Is Hawking radiation determined by a global event horizon? by a local apparent horizon? Global: Don Page, Roger Penrose, Stephen Hawking (?), Local: Parikh and Wilczek, Matt Visser, Tim Clifton, Alex Nielsen, Paranjape and Padmanabhan, “Essential and inessential features of Hawking radiation” M Visser International Journal of Modern Physics D 12 (04), 649-661 (2003)
Karl Schwarzschild Meeting 2015, FIAS 10 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Cannot be checked in the Schwarzschild solution: a degenerate case where they coincide. Then yes its given off from the event horizon, but maybe because its an apparent horizon.
The first key issue Local or global horizons?
The big issue: Is Hawking radiation determined by a global event horizon? by a local apparent horizon? Global: Don Page, Roger Penrose, Stephen Hawking (?), Local: Parikh and Wilczek, Matt Visser, Tim Clifton, Alex Nielsen, Paranjape and Padmanabhan, “Essential and inessential features of Hawking radiation” M Visser International Journal of Modern Physics D 12 (04), 649-661 (2003) In former case: don’t know where event horizon is: won’t be determined till end of universe e.g. Galaxy BH merge with Andromeda BH. So how does the local physics know when/where to emit radiation?
Karl Schwarzschild Meeting 2015, FIAS 10 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 The first key issue Local or global horizons?
The big issue: Is Hawking radiation determined by a global event horizon? by a local apparent horizon? Global: Don Page, Roger Penrose, Stephen Hawking (?), Local: Parikh and Wilczek, Matt Visser, Tim Clifton, Alex Nielsen, Paranjape and Padmanabhan, “Essential and inessential features of Hawking radiation” M Visser International Journal of Modern Physics D 12 (04), 649-661 (2003) In former case: don’t know where event horizon is: won’t be determined till end of universe e.g. Galaxy BH merge with Andromeda BH. So how does the local physics know when/where to emit radiation? Cannot be checked in the Schwarzschild solution: a degenerate case where they coincide. Then yes its given off from the event horizon, but maybe because its an apparent horizon. Karl Schwarzschild Meeting 2015, FIAS 10 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 If its local: Which apparent horizon? IMOTS or OMOTS?
If its local: which apparent horizon? There are two! - Inner and outer. Put it in cosmological context: cannot be the outer one because of infalling radiation If inner one: then Hawking radiation is trapped (arXiv:1310.4771) But it turns out this horizon does not emit Hawking radiation (Firouzjae and GE: arXiv:1407.3577) Allow for case of dynamic horizon: backreaction, no Killing vectors, no bifurcating Killing horizon (can’t use exponential rescaling of affine parameter relative to Killing parameter)
Karl Schwarzschild Meeting 2015, FIAS 11 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 The bifurcating event horizons
Figure: Bifurcation of the event horizons
MOTS surfaces separate domains with θ+ > 0 and θ+ < 0, so they have to come in pairs. They intersect in IMOTS 2-sphere. Karl Schwarzschild Meeting 2015, FIAS 12 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 The location of the event horizons
Where is outgoing null divergence zero: θ+ = 0? Use 1+1+2 covariant formalism “Astrophysical Black Hole horizons in a cosmological context: Nature and possible consequences on Hawking Radiation” GE, R Goswami, A I M Hamid, S D Maharaj Phys. Rev. D 90, 084013 (2014) arXiv:1407.3577
Karl Schwarzschild Meeting 2015, FIAS 13 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Cosmological context: Effect of infalling radiation
Mass increases so Schwarzschild radius RH = 2M increases: R˙H > 0 OMOTS surface becomes spacelike
Figure: Incoming radiation makes the OMOTS spacelike.
This separates event horizon and apparent horizon. Karl Schwarzschild Meeting 2015, FIAS 14 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Cosmological context: Effect of infalling radiation Penrose diagram
Figure: Penrose diagram: Incoming radiation makes the OMOTS spacelike
Event horizon moves out to include apparent horizon. IMOTS is timelike. Karl Schwarzschild Meeting 2015, FIAS 15 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Effect of cosmological constant The real cosmological context
Figure: Cosmological constant decouples event horizons from black hole
The real universe is not asymptotically flat! Karl Schwarzschild Meeting 2015, FIAS 16 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Virtual Pair production: Hawking (SciAm 1976) Tunnelling: Parikh and Wilczek (Parikh and Wilczjek PRL 2000) S-matrix, Super-Scattering operator (Hawking 1974, PRD 1976)
Cosmological context: Effect of infalling radiation Turns Hawking radiation off
Incoming radiation makes the OMOTS spacelike This should turn radiation off.
Karl Schwarzschild Meeting 2015, FIAS 17 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Tunnelling: Parikh and Wilczek (Parikh and Wilczjek PRL 2000) S-matrix, Super-Scattering operator (Hawking 1974, PRD 1976)
Cosmological context: Effect of infalling radiation Turns Hawking radiation off
Incoming radiation makes the OMOTS spacelike This should turn radiation off. Virtual Pair production: Hawking (SciAm 1976)
Karl Schwarzschild Meeting 2015, FIAS 17 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 S-matrix, Super-Scattering operator (Hawking 1974, PRD 1976)
Cosmological context: Effect of infalling radiation Turns Hawking radiation off
Incoming radiation makes the OMOTS spacelike This should turn radiation off. Virtual Pair production: Hawking (SciAm 1976) Tunnelling: Parikh and Wilczek (Parikh and Wilczjek PRL 2000)
Karl Schwarzschild Meeting 2015, FIAS 17 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Cosmological context: Effect of infalling radiation Turns Hawking radiation off
Incoming radiation makes the OMOTS spacelike This should turn radiation off. Virtual Pair production: Hawking (SciAm 1976) Tunnelling: Parikh and Wilczek (Parikh and Wilczjek PRL 2000)
S-matrix, Super-Scattering operator (HawkingKarl 1974, Schwarzschild PRD Meeting 1976) 2015, FIAS 17 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 IMOTS or OMOTS?
Figure: Maybe IMOTS radiates even if OMOTS does not.
Particle picture suggests yes. But field calculation says no (Firouzjaee). Karl Schwarzschild Meeting 2015, FIAS 18 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Particle picture gives 100% on or off Field picture allows fuzzier limits Actually: need energy momentum tensor to check what is happening (Davies, Perry) In the meantime: can use the eikonal approximation [1408.0778] NB: not static spacetime can’t rely on Killing vectors and associated properties NB: does it happen in the vacuum or in the fluid?
Key point: particle or field
One can use particle or field picture
Karl Schwarzschild Meeting 2015, FIAS 19 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Field picture allows fuzzier limits Actually: need energy momentum tensor to check what is happening (Davies, Perry) In the meantime: can use the eikonal approximation [1408.0778] NB: not static spacetime can’t rely on Killing vectors and associated properties NB: does it happen in the vacuum or in the fluid?
Key point: particle or field
One can use particle or field picture Particle picture gives 100% on or off
Karl Schwarzschild Meeting 2015, FIAS 19 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Actually: need energy momentum tensor to check what is happening (Davies, Perry) In the meantime: can use the eikonal approximation [1408.0778] NB: not static spacetime can’t rely on Killing vectors and associated properties NB: does it happen in the vacuum or in the fluid?
Key point: particle or field
One can use particle or field picture Particle picture gives 100% on or off Field picture allows fuzzier limits
Karl Schwarzschild Meeting 2015, FIAS 19 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 In the meantime: can use the eikonal approximation [1408.0778] NB: not static spacetime can’t rely on Killing vectors and associated properties NB: does it happen in the vacuum or in the fluid?
Key point: particle or field
One can use particle or field picture Particle picture gives 100% on or off Field picture allows fuzzier limits Actually: need energy momentum tensor to check what is happening (Davies, Perry)
Karl Schwarzschild Meeting 2015, FIAS 19 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 NB: not static spacetime can’t rely on Killing vectors and associated properties NB: does it happen in the vacuum or in the fluid?
Key point: particle or field
One can use particle or field picture Particle picture gives 100% on or off Field picture allows fuzzier limits Actually: need energy momentum tensor to check what is happening (Davies, Perry) In the meantime: can use the eikonal approximation [1408.0778]
Karl Schwarzschild Meeting 2015, FIAS 19 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 NB: does it happen in the vacuum or in the fluid?
Key point: particle or field
One can use particle or field picture Particle picture gives 100% on or off Field picture allows fuzzier limits Actually: need energy momentum tensor to check what is happening (Davies, Perry) In the meantime: can use the eikonal approximation [1408.0778] NB: not static spacetime can’t rely on Killing vectors and associated properties
Karl Schwarzschild Meeting 2015, FIAS 19 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Key point: particle or field
One can use particle or field picture Particle picture gives 100% on or off Field picture allows fuzzier limits Actually: need energy momentum tensor to check what is happening (Davies, Perry) In the meantime: can use the eikonal approximation [1408.0778] NB: not static spacetime can’t rely on Killing vectors and associated properties NB: does it happen in the vacuum or in the fluid?
Karl Schwarzschild Meeting 2015, FIAS 19 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Effect on fluid rather than vaccum
Figure: Incoming field goes through dynamic fluid and emerges to future
Hawking, Birrell and Davies say effect is due to dynamic fluid: but calculate in static Schwarzschild solutins Karl Schwarzschild Meeting 2015, FIAS 20 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Paper 1: : Javad T. Firouzjaee and GE arXiv:1408.0778
Cosmic Matter Flux May Turn Hawking Radiation Off Javad T. Firouzjaee, George F. R. Ellis An astrophysical (cosmological) black hole forming in a cosmological context will be subject to a flux of infalling matter and radiation, which will cause the outer apparent horizon (a marginal trapping surface) to be spacelike. As a consequence the radiation emitted close to the apparent horizon no longer arrives at infinity with a diverging redshift. Standard calculations of the emission of Hawking radiation then indicate that no blackbody radiation is emitted to infinity by the black hole in these circumstances, hence there will also then be no black hole evaporation process due to emission of such radiation as long as the matter flux is significant
Karl Schwarzschild Meeting 2015, FIAS 21 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Eikonal approximation
Consider the eikonal equation for the wave ϕ = A(t, r)e±iψ. It is known that kµ = ∇µψ , the normal vector of the constant phase plane, describes wave propagation, and is a null geodesic vector. Let us expand the wave phase near the eikonal approximation case ψ 1: dxµ ψ = ψ + ∇ ψdxµ = k dλ 0 µ µ dλ = νdλ = (1 + z)ν0dλ. (1) This shows that the phase of the wave near the infinite redshift surface is very big: ψ 1. According to the discussion by Visser (2003), the eikonal (geometric optics) approximation is an essential feature for occurrence of black hole radiation. Therefore, having geometric optics valid in the close vicinity of the apparent horizon is a necessary condition for demonstrating existence of Hawking radiation by the eikonal method. We now see that we can use existence of an infinite or very large redshift surface as a criterion for when this is satisfied. Karl Schwarzschild Meeting 2015, FIAS 22 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Eikonal approximation arXiv:1407.3577
The essential adiabatic condition (eikonal approximation) for black hole radiation gives a strong limit to the black holes that can emit Hawking radiation. We consider the special case of the cosmic blackbody radiation (CBR) influx (which exists everywhere in the universe). At a very late stage of black hole formation when the CBR influx decays away, the black hole horizon becomes first a slowly evolving horizon and then an isolated horizon; at that stage, black hole radiation will start. This study suggests that the primordial black hole evaporation scenario should be revised to take these considerations into account. The inner horizon is timelike while the continuous CBR influx into the black hole makes the outer horizon spacelike. This means Hawking radiation in realistic astrophysical contexts is suppressed while the infalling radiation is appreciable.
Karl Schwarzschild Meeting 2015, FIAS 23 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Spacelike MOTS does not radiate
Figure: Spacelike MOTS does not radiate while infalling radiation matters so horizon is dynamic.
At late times it becomes an isolated horizon and radiation can start. Karl Schwarzschild Meeting 2015, FIAS 24 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 The function C arXiv:1407.3577
Let V a be tangential to the MOTS hypersurface H and orthogonal to the foliation by marginally trapped surfaces. It is always possible to find a function C and normalization of `a such that V a = `a − Cna. The a definition of V implies that LV θ` = 0, which gives an expression for C: L θ C = ` ` . Lnθ` When C < 0 the apparent horizon is an IMOTS and C > 0 the apparent horizon is an OMOTS, and if C = 0 it becomes an event (isolated) horizon. The value for the C function is important because it shows the type of the black hole horizon. It shows if a MOTS surface is an OMOTS or IMOTS surface and whether it is timelike or spacelike, and specially it is a criterion for where the adiabatic approximation is satisfied.
Karl Schwarzschild Meeting 2015, FIAS 25 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 The value of C Backreaction effects
Assume that there is no infalling flux except the CBR flux, we consider now possible backreaction effects. Let us compare the outgoing Hawking radiation flux which decreases the black hole mass, when that radiation is being emitted, with the infalling CBR flux, which cause black holes to grow. If the CBR flux is greater than the Hawking radiation flux the OMOTS remains space like, and if the radiating flux is greater than the CBR flux, the OMOTS will eventually change to a timelike apparent horizon. Now the question is what is the magnitude of the C function for the Hawking radiation flux? The C function becomes negative, giving a timelike surface for the Hawking radiation-only case: G C = − A (ρ + p) . c4 AH HR
Karl Schwarzschild Meeting 2015, FIAS 26 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 The relevant masses arXiv:1407.3577
−8 M The black hole temperature is T = 6 × 10 M k. For a solar mass black hole CHR = 10−32 at the present time, which is CCBR −8 very small. For black holes with mass M > 10 M the infalling CBR flux is greater than the radiation flux and OMOTS remains spacelike.
−8 Only for a black hole with mass M < 10 M are the two fluxes comparable and the black hole can have radiation which decreases the black hole area. This actually rules out astrophysical black hole radiation backreaction effects that could make the OMOTS surface timelike, if there indeed is any Hawking radiation. Hence for such black holes the OMOTS surface is necessarily inside the classical event horizon. Suppression stronger in past (CBR 3K): It will be less in future (CBR 3K) Karl Schwarzschild Meeting 2015, FIAS 27 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Paper 2: Javad T. Firouzjaee and GE arXiv 1503.05020
Among the different methods to derive particle creation, finding the quantum stress tensor expectation value gives a covariant quantity which can be used for examining the back-reaction issue. However this tensor also includes vacuum polarization in a way that depends on the vacuum chosen. Here we review different aspects of particle creation by looking at energy conservation and at the quantum stress tensor. It is shown that in the case of general spherically symmetric black holes that have a dynamical horizon, as occurs in a cosmological context, one cannot have pair creation on the horizon because this violates energy conservation. This confirms the results obtained in other ways in the previous paper.
Karl Schwarzschild Meeting 2015, FIAS 28 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 The stationary case
Consider the possibility of particle creation by a stationary gravitational µ µ field. The energy of a particle in such a field is E = −pµξ where p is the four-momentum of the particle, and ξµ is the Killing vector field. The energy E of a particle is always positive outside the black hole horizon, where the Killing vector is timelike. The Killing vector is spacelike inside the Killing horizon ξ2 = 0, and the energy is negative there. Therefore, this allows particle pair creation just around the Killing horizon. On the other hand, we know that a Killing horizon in a stationary spacetime is necessarily an event horizon (see Hawking and Ellis, proposition 9.3.6). Hence, one can expect particle creation in a stationary spacetime which contains a black hole.
Karl Schwarzschild Meeting 2015, FIAS 29 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 The dynamical case: Energy conservation
In the dynamical case the question is how does energy conservation work for pair creation around a dynamical black hole. It is not possible to define a conserved quantity E for an evolving space time, as it does not have a Killing vector field. But locally for a vector field Uµ(x) that is timelike outside the black hole, we can define the particle’s energy relative to an observer with 4-velocity µ µ U as E = −pµU . For instance, in a general spherical symmetry spacetime, one can define µ µ the energy E = −pµK of the particle relative to the Kodama vector K , which in the stationary case becomes the same as the Killing vector.
Karl Schwarzschild Meeting 2015, FIAS 30 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 The dynamical case: Energy conservation
Consider pair creation around the OMOTS (Outer Marginally Trapped 3-Surface) when there is infalling radiation or matter, so this surface is spacelike. Since the particle – antiparticle pair will be located inside the horizon and will each have energy defined relative to the same timelike vector, the energy E for both particles will have the same sign. As a result, any long-lived particle creation violates the energy conservation around the OMOTS. Hence Hawking radiation will not occur there
Karl Schwarzschild Meeting 2015, FIAS 31 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 The isolated horizon case
When the matter flux becomes very small, the black hole apparent horizon becomes an isolated horizon where its tangent vector becomes a null vector `µ and it becomes a null surface. Note that a Killing horizon assumes the existence of a Killing vector field in some neighborhood of the horizon, but the isolated horizon is defined only in terms of the intrinsic and extrinsic geometry of the horizon itself, where `µ is a Killing vector for the intrinsic geometry of horizon. To consider energy conservation for pair creation around the isolated horizon, we limit ourselves to the general spherically symmetric dynamic black hole.
Karl Schwarzschild Meeting 2015, FIAS 32 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Black Hole Radiation is turned off by infalling radiation
Figure: Black hole outgoing waves
Karl Schwarzschild Meeting 2015, FIAS 33 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Kodama vector (Faraoni)
The Kodama Vector generalizes the notion of a Killing vector field to spherically symmetric spacetimes which do not have one. With metric 2 a b 2 2 ds = habdx dx + R dΩ(2)
and ab the volume form of the timelike 2-metric hab, the Kodama vector is defined as
a ab θ φ a K = ∇bR ⇒ K = K = 0, ∇aK = 0
This implies the Kodama energy current is conserved:
a ab a J := G Kb ⇒ ∇ Ja = 0
even if there is no timelike Killing vector. In a static spacetime the Kodama vector is parallel to the timelike Killing vector.
Karl Schwarzschild Meeting 2015, FIAS 34 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Isolated Horizons
Consider that the collapsing fluid within a compact spherically symmetric spacetime region will be described by the following metric in the comoving coordinates (t, r, θ, ϕ):
ds2 = −e2ν(t,r)dt2 + e2ψ(t,r)dr 2 + R(t, r)2dΩ2. (2)
The Kodama vector for this metric is
K µ = e−(ν+ψ)(R0, −R˙ , 0, 0). (3)
Using the Einstein equations one can show that the norm of the Kodama vector is 2M K K µ = ( − 1), (4) µ R where M is the Misner-Sharp mass for the spherically symmetric model. This vector is spacelike inside the apparent horizon and timelike outside it.
Karl Schwarzschild Meeting 2015, FIAS 35 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Isolated Horizons
µ Using the energy definition E = −pµK , one can show that the energy of the particle outside the isolated horizon is positive and the energy of the particle inside is negative. Hence, one can have pair particle creation for isolated horizons without violating energy conservation. While we have shown this using the Kodama vector for reference, that is for convenience and is not essential; some other timelike vector field could be used for general spacetime.
Karl Schwarzschild Meeting 2015, FIAS 36 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Hawking, 1401.5761 “Information Preservation and Weather Forecasting for Black Holes” Mersini-Houghton, 1406.1525, 1409.1837 “ Back-reaction of the Hawking radiation flux on a gravitationally collapsing star” Bardeen, 1406.4098 “Black hole evaporation without an event horizon”
Does a singularity occur?
Hawking radiation in realistic astrophysical contexts is suppressed while the infalling radiation is appreciable. However eventually in the far future the infalling radiation dies away. At that point Hawking radiation may start up. If so it can eat away at the central mass before a singularity has occurred. This may or may not be sufficient to entirely do away with the singularity. Some have suggested this is so:
Karl Schwarzschild Meeting 2015, FIAS 37 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Mersini-Houghton, 1406.1525, 1409.1837 “ Back-reaction of the Hawking radiation flux on a gravitationally collapsing star” Bardeen, 1406.4098 “Black hole evaporation without an event horizon”
Does a singularity occur?
Hawking radiation in realistic astrophysical contexts is suppressed while the infalling radiation is appreciable. However eventually in the far future the infalling radiation dies away. At that point Hawking radiation may start up. If so it can eat away at the central mass before a singularity has occurred. This may or may not be sufficient to entirely do away with the singularity. Some have suggested this is so: Hawking, 1401.5761 “Information Preservation and Weather Forecasting for Black Holes”
Karl Schwarzschild Meeting 2015, FIAS 37 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Bardeen, 1406.4098 “Black hole evaporation without an event horizon”
Does a singularity occur?
Hawking radiation in realistic astrophysical contexts is suppressed while the infalling radiation is appreciable. However eventually in the far future the infalling radiation dies away. At that point Hawking radiation may start up. If so it can eat away at the central mass before a singularity has occurred. This may or may not be sufficient to entirely do away with the singularity. Some have suggested this is so: Hawking, 1401.5761 “Information Preservation and Weather Forecasting for Black Holes” Mersini-Houghton, 1406.1525, 1409.1837 “ Back-reaction of the Hawking radiation flux on a gravitationally collapsing star”
Karl Schwarzschild Meeting 2015, FIAS 37 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Does a singularity occur?
Hawking radiation in realistic astrophysical contexts is suppressed while the infalling radiation is appreciable. However eventually in the far future the infalling radiation dies away. At that point Hawking radiation may start up. If so it can eat away at the central mass before a singularity has occurred. This may or may not be sufficient to entirely do away with the singularity. Some have suggested this is so: Hawking, 1401.5761 “Information Preservation and Weather Forecasting for Black Holes” Mersini-Houghton, 1406.1525, 1409.1837 “ Back-reaction of the Hawking radiation flux on a gravitationally collapsing star” Bardeen, 1406.4098 “Black hole evaporation without an event horizon”
Karl Schwarzschild Meeting 2015, FIAS 37 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Does an event horizon occur? The radiation decreases the fluid mass
Mass decreases so Schwarzschild radius RH = 2M decreases: R˙H < 0
Figure: Negative energy radiation causes a backreaction effect.
Nb need dynamic spacetime representation: 4 TH = 1/(8πM) = 1/(4πRH ) ⇒ ρH ∝ 1/RH . Karl Schwarzschild Meeting 2015, FIAS 38 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Option 1: no singularity occurs No event horizon occurs
Figure: Negative energy Hawking radiation might eat the fluid away completely.
Competition between collapse of fluid and Hawking radiation eating away at central mass: which occurs first? There may be no event horizon and no information loss. Karl Schwarzschild Meeting 2015, FIAS 39 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Option 2: Evaporation does not happen Singularity may remain
Figure: The radiation may not succeed in getting rid of the singularity
Fluid collapse may win. Note that this is a dynamic spacetime with backreaction, and radiation going both in and out (so not Vaidya). Information is lost down the black hole. Karl Schwarzschild Meeting 2015, FIAS 40 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 While infalling radiation is significant, no Hawking radiation will take place, Eventually it will start. It then may or may not succeed in eating away the central mass so no singularity results. If it does not succeed a spacetime singularity may remain - or a quantum gravity bounce into another domain.
To be done
To get a conclusive result, one needs a calculation of the backreaction effect of the stress-energy tensor of the Hawking radiation in a dynamic spacetime where the interaction of the radiation with the central fluid is fully taken into account. It must use the Unruh vacuum rather than Boulware or Hartle-Hawking. This will almot scertainly require numerical integration. Until this is done the outcome remains open: It may solve the information loss problem.
Karl Schwarzschild Meeting 2015, FIAS 41 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Eventually it will start. It then may or may not succeed in eating away the central mass so no singularity results. If it does not succeed a spacetime singularity may remain - or a quantum gravity bounce into another domain.
To be done
To get a conclusive result, one needs a calculation of the backreaction effect of the stress-energy tensor of the Hawking radiation in a dynamic spacetime where the interaction of the radiation with the central fluid is fully taken into account. It must use the Unruh vacuum rather than Boulware or Hartle-Hawking. This will almot scertainly require numerical integration. Until this is done the outcome remains open: It may solve the information loss problem.
While infalling radiation is significant, no Hawking radiation will take place,
Karl Schwarzschild Meeting 2015, FIAS 41 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 If it does not succeed a spacetime singularity may remain - or a quantum gravity bounce into another domain.
To be done
To get a conclusive result, one needs a calculation of the backreaction effect of the stress-energy tensor of the Hawking radiation in a dynamic spacetime where the interaction of the radiation with the central fluid is fully taken into account. It must use the Unruh vacuum rather than Boulware or Hartle-Hawking. This will almot scertainly require numerical integration. Until this is done the outcome remains open: It may solve the information loss problem.
While infalling radiation is significant, no Hawking radiation will take place, Eventually it will start. It then may or may not succeed in eating away the central mass so no singularity results.
Karl Schwarzschild Meeting 2015, FIAS 41 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 To be done
To get a conclusive result, one needs a calculation of the backreaction effect of the stress-energy tensor of the Hawking radiation in a dynamic spacetime where the interaction of the radiation with the central fluid is fully taken into account. It must use the Unruh vacuum rather than Boulware or Hartle-Hawking. This will almot scertainly require numerical integration. Until this is done the outcome remains open: It may solve the information loss problem.
While infalling radiation is significant, no Hawking radiation will take place, Eventually it will start. It then may or may not succeed in eating away the central mass so no singularity results. If it does not succeed a spacetime singularity may remain - or a quantum gravity bounce into another domain. Karl Schwarzschild Meeting 2015, FIAS 41 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 References
1408.0778: “Cosmic Matter Flux May Turn Hawking Radiation Off” Firouzjaee and GE 1407.3577: “Astrophysical Black Hole horizons in a cosmological context” GE, Goswami, Hamid, Maharaj 1503.05020: “Particle creation from the quantum stress tensor” Firouzjaee and GE
Karl Schwarzschild Meeting 2015, FIAS 42 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Eternal black holes
In the case of eternal black holes, the obvious statement of the black hole evaporation hypothesis in terms of Cauchy data is inconsistent with the symmetry of the maximally extended Kruskal-Schwarzschild solution. The implication is that in this case too, the black hole does not evaporate: same kind of solution holds Needs checking: is vacuum in-state invariant under space-time symmetry group? If not why not? This case is not realistic but serves as test bed for calculations NB: same kind of issue arises for Unruh radiation; - its a global effect and cannot be realised in practice. - what about De Sitter and Gibbons-Hawking radiation?
Karl Schwarzschild Meeting 2015, FIAS 43 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Symmetries of eternal black holes
Figure: Left-right, future-past and boost symmetries. Which direction should Hawking radiation occur?
Karl Schwarzschild Meeting 2015, FIAS 44 George Ellis (University of Cape Town) Black Hole Evaporation? / 45 Paper 2 arXiv 1503.05020
Looking at the expectation value of the quantum stress tensor with three different definitions of the vacuum state, we study the nature of particle creation and vacuum polarization in black hole and cosmological models, and the associated stress energy tensors. We show that the thermal temperature that is calculated from the particle flux given by the quantum stress tensor is compatible with the temperature determined by the affine null parameter approach. Finally, it will be shown that in the spherically symmetric dynamic case, we can neglect the backscattering term and only consider the s-waves term near the future apparent horizon.
Karl Schwarzschild Meeting 2015, FIAS 45 George Ellis (University of Cape Town) Black Hole Evaporation? / 45