PoS(PLANCK 2015)057 http://pos.sissa.it/ † ∗ [email protected] Speaker. The author thanks the School of Social and Applied Sciences for support to attend Planck 2015 This paper puts forward a conjecture thata there mechanism are to no prevent black black holes hole inviable M formation high theory. is energy We needed model will show in of that quantum 4regulation gravity. dimensions mechanism Black to hole based make formation string on may theory string beby a condensation. averted ‘hot by holograms’ a In that gravity this form scenario,the during properties black gravitational of holes collapse. free are thermalon The replaced solutions geometrichologram that conditions to are based occur, proposed however, on for are conversion to localspace. a and high This generic temperature idea in can dimension beevaporation, and applied could which to apply appears resolve throughout to the M problems bethe presented conventional inconsistent view, by black with the holes quantum process areproposed information of real here black theory. and that hole firewalls situation are would Whereas, be probably in reversed. a chimera, in the scenario ∗ † Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). 18th International Conference From the Planck25-29 Scale May to 2015 the Electroweak Scale Ioannina, Greece M. Hewitt String condensation: Nemesis of Black Holes? Canterbury Christ Church University E-mail: PoS(PLANCK 2015)057 n 5, = (3.1) (3.2) d ] is that 2 M. Hewitt k y n x k , n g 1 = k , ∞ 1 ∑ = so that the string entropy n 3 1 − = d i 2 M x ∝ ) ) + k A 1 + − ∝ y 2 2 1 k − + d )( y ]. Four different possibilities for the nature R 1 ( ] avoids the issues associated with horizons 1 i is the number of uncompactified spacetime 5 x ∝ + d k 2 3 ], as high energy collisions would form black − − − 2 7 d d 1 )( 2 1 1 M ∞ = i ∏ − k ∝ , , where n = 3 3 g 1 − 1 − ) d d 1 − − k M , y i n MM x g ( ∝ 1 − ∞ = S 1 ∑ 1 k ]. The fuzzball model [ )( ]. 4 y scales as 6 i ][ x R 3 ] − 7 1 4 the excited string states occupy a region larger than a black hole with the ( 1 > ∞ = i ∏ d ) = y , x 4 a typical excited string state would be hidden by a horizon (see section 4). ( G ≤ measures the critical gravity hypersurface, consistent with a higher dimensional version d A An attractive feature of string theory is that it naturally includes gravitons and has finite am- There has been a recent revival of interest in the nature of black holes and debate over the The black hole radius The gravitational blue shift at a critical acceleration surface is encodes the distribution of spin againstis level number. The total squared spin for all states at level plitudes for graviton scattering inby the an critical infinite dimension. spectrum Highquantum of energy gravity free scattering is is string problematic intermediated states. in 4 However, dimensions string [ theory as a perturbative theory of 3. Strings in 4 dimensions holes rather than demonstrate string scatteringThe amplitudes generating or function the [ production of long string states. has the scaling where of the holographic principle [ of the collapsed state may beconventional identified view, with which and may without be horizon, extended with to and the without black a hole firewall. complementarity The principle [ nature of the horizon prompted by the firewall paradox [ String condensation: Nemesis of Black Holes? 1. Introduction a real horizon formssmall during magnitude collapse, of the but Riemannian is tidalduring curvature. not the However, problems distinguished evaporation with locally. process quantum information havelocally This led detectable firewall is to [ suggestions supported that byand the the singularities, horizon and may these advantages be arestring surrounded shared condensation by by leads a the to proposal formation presentedgravitational here of collapse. that quasi a 2 In process dimensional this of closed hot sense, horizon, string would firewalls regions not. would as be end real, points but of black holes, characterised2. by Scaling a behaviour vs dimension dimensions, so for and for same mass, and so can be taken as stable against gravitational collapse. The marginal case is PoS(PLANCK 2015)057 ]. 7 (3.7) (3.8) (3.9) (3.3) (3.4) (3.5) (3.6) (3.10) M. Hewitt G 1 → ) lim y x k n ( , x n p N 1 ) g n 2 n σ √ / n k 1 1 2 x √ y γ 2 ∞ ∞ = n π ∑ γ n ) n q 1 − ( x ∞ y 6 ∑ 1 = x ∼ ∂ k ∂ ∞ ∂ = − ∂ ∑ 1 On taking this limit, we find n = 2 N exp 3 y 1 x i ( 3 β . This implies that the angular momentum of most 1 ∼ 3 = → X − ˆ = ∞ nG = N h is R k ∏ n n y , 1 ˆ = 3 n n 2 G α 2 → g ˆ 1 is 3 y X = J 2 ) = ∼ 3 lim → k 2 N y lim N y 1 n i , = q ∞ = x R ∑ k ( h G R 6 2 ˆ G J on the generating function 1 2 ˆ → J lim y for level number is given by n so that the greatest density of strings and information would be around the self-dual β is the partition function for the other oscillators. Now ) ] it was noted that for heterotic strings, thermal duality implies that there is a maximum x 7 ( p against In [ It appears that most string states would collapse behind event horizons. However, the fixed Z where temperature, and it was suggestedare that essentially the thin shells. heterotic string Thisextended idea states to is in non-heterotic elaborated 4 strings below and uncompactified in other dimensions the dimensions. context of string condensation, and nature of the valueimplies for that the the free transition spectrum temperaturepossibility is of calculated somehow a preserved from bag when model the gravity interpretation for isquasi-free thermalon string turned quarks states winding on. and in mode gluons 4 This are dimensions supports in confinednormal the analogy to vacuum. to hadrons, QCD, which where are regions of a different phase to the where asymptotically and of The generating function for eigenstates of String condensation: Nemesis of Black Holes? or The operator for squared spin and the operator ˆ and total values are found by taking the limit so that the average squared spinstring at states level is too small to prevent collapse, and a similar result holds for the electric charge [ PoS(PLANCK 2015)057 M. Hewitt ].The information con- 9 ], in thermal equilibrium 9 4 ] describes a string condensate that forms at the ] the conventional picture of black hole evaporation 11 8 ][ 10 ]. It is the Euclidean single wrapping mode related to the 15 ][ 14 ]. The thermalon or thermal scalar has an interpretation in terms of a ][ 10 13 ][ 12 bits exceeds the holographic limit during collapse inside the horizon before 60 10 ∼ The thermalon or thermal scalar [ There is also an issue with holographic principle for stellar collapse [ Theorem 2: A contradiction exists between: 2.a) completely unitarily evaporating black holes, Theorem 1: A contradiction exists between: 1.a) completely unitarily evaporating black holes, While the issue of gravitational collapse for single strings discussed in the previous section tent of star 5. The thermalon and hot strings thermal path integral for a singlea string. macroscopic The order thermalon parameter, is and not a providesThe normal thermalon an propagating mode effective state can theory but be of rather interpreted thewith as thermal a the string deformation normal condensate. of the vacuum. vacuumby [ There warp is factor or a energy continuous [ micro-canonical family ensemble of of strings, solutions, as which it can can be be shown parametrized to describe their time averaged properties reaching the singularity. Stringterpretation, physics so that is the apparently conventional notprinciple collapse unless relevant process information at becomes begins to this inconsistent be with point, destroyed the before in holographic the the singularity is usual reached. in- Hagedorn transition [ 2.b) large black holes arenally, described a by large local black physics holeevaporation). (no should signals resemble faster its than classical light) theoretical and counterpart 2.c) (aside from exter- its slow 1.b) a freely falling observer noticeshorizon, nothing special and until 1.c) the they pass black well holethe within interior a exponential Hilbert large of space black dimensionality the hole’s may Bekenstein be Hawking well entropy. approximated as appears to be inconsistent with unitarity. applies to 4 dimensions, gravitationalmension. collapse presents To problems resolve for short multiincreasing distances string energy, requires states eventually in gravity concentrating becomes any high strong di- energyteriorates over again. into longer Making distances, a gravity and small consistent the with volumeand resolution quantum - macroscopic mechanics de- collapsed at is objects problematic will for also thistional reason, be regulator present mechanism for should d>4. generalise We therefore toas expect all all that regions will a of gravita- have M collapsed theory states,general and problem and all with so compactifications, black need holes to ina avoid terms paradoxes photon of associated information trap with theory without is black inappears propagating holes. getting to information The be information inconsistent faster out with from than the principles lighting of to (outside quantum the information the theory. Braunstein light For - example, cone) Pirandola accord- and theorems this [ String condensation: Nemesis of Black Holes? 4. Black hole paradoxes PoS(PLANCK 2015)057 is E (6.2) (5.1) (5.3) (5.4) (6.1) (5.2) M. Hewitt ]: φ ) 2 10 ] related to the string charge 6 ε 2 10 / − 3 ) 2 ) r E 2 4 π H H ( β β + e ) ( 6 2 GA r 2 1 ) shell − π 4 ε e µν 2 µν 2 r 2 2 − S δ G / B r δ 3 on − 4 δ = = ( | δ ) ( shell E 2 − π + φ G H dr µν 2 ( k th β 2 on exp )) 5 √ r J T where 1 − G r r 4 ( e µβ − ∝ w ∝ √ ] = β ∞ G k dependent: ε ( 0 2 E = 1 τ 2 e 16 i Z r √ J = ) = ( m − µν r e µν e ≈ ( φ J w GA = T 2 E h π i m r 4 ∂ ∂φ µν e ∼ r 1 T h A + is effectively 2 πδ φ ]. r 2 2 m ∂ ∂ 11 ][ 10 ] 16 thermalon charge used in the superconductor model of [ is a small parameter. ) ε 1 ] . The thermalon also gives an effective description of the average string charge density, with ( These are relevant to the beginning of the proposed conversion process, and show that there The heterotic thermalon field equation in Rindler coordinates is [ The area difference across the solution is given by This can be described by the warp factor The thermalon description gives a good approximation where the energy of the condensate is U ]. The average stress tensor for a microcanonical ensemble of strings with total energy 10 16 is no energy barrier to initiatingneglect conversion. interactions [ For small values of the thermal string density we can where and 6. Thermalon weak field solutions related to the on-shell thermalon value by [ where the thermalon mass This admits the following finite accelerating wall solution where the String condensation: Nemesis of Black Holes? [ current by [ large, which will be the casein [ if the kinetic energy of collapse is converted into string, as proposed PoS(PLANCK 2015)057 ] 17 (6.3) (6.4) (6.5) ][ 10 M. Hewitt , and no inter- ]. The existence M 10 ] . In this case, the 10 ] that leads to the possibil- 11 ]. This shows that contrary to rather than log ], [ 0 17 α ) / 10 1 2 ], [ ( ρ 9 0 O − α e / ) 2 0 2 ρ α ρ − 0 e α 0 − 0 / 2 α E 2 2 α ρ ( 2 0 √ − The thermalon can be seen as part of the gravity r e 6 α E ) ε = ]. and in particular the energy density is given by 2 γ √ < , E ∼ 11 i − ρ W ) ( ψ x = ( E ρρ i e ) T x h ( ττ e ], thermal duality not is not directly required for a self-supporting T h 10 ] This condensate is self-supporting due to negative energy on the inside 9 ], allowing the possibility of a conversion process as the interior shrinks [ For heterotic strings the left moving currents and their interaction vertex, at the dual point, the Type II strings show similar behaviour [ 16 ][ 9 sector in string theory generally,action. and gravity The becomes condensate part that of formsas at a it the combined can Hagedorn ‘gravito-thermal’ be transition inter- described behaves by as part the of thermalon. the A gravity string sector condensate may form near black hole [ 7. Gravito-thermal interaction pair (thermalon, graviton) is equivalent to action is required for a self-supportingsame condensate. in Further the investigation heterotic may case, showstring rather that condensate this than shell is the has the superconducting ais ball conical picture still rather of than proportional [ hyperbolic to geometry. areaalso implies The for that volume the (some of generalisation final the of) state, stringregulator interior or for with brane 11 condensation entropy dimensional also proportional supergravity. provides a to gravitational area. Our conjecture or possibly replace it [ of such states augmented by aconversion coating process. of string For condensate such is aintroduce a condensate static key stepping to energy stone form, at to we the thethat propose Hagedorn there proposed that is point an it near automatic is a conversionfurther not of black that matter necessary the hole in to final free as state gently fall will might to behorizon. be produce essentially A such composed expected, demonstration a of of but this string the rather condensate condensate, conversion withoutlink and effect a through in closed concrete the trapping calculation programme is proposed the here. main missing [ condensate to form. For type II strings, the shell thickness is which is negative for with positive radial pressure for the type II thermalon solution ity of a self-supporting condensate aroundthe a expectation collapsed expressed object in [ [ String condensation: Nemesis of Black Holes? thus having the qualitative behaviour found for heterotic strings [ PoS(PLANCK 2015)057 (8.5) (8.4) (8.1) M. Hewitt the timelike unit 0 E then the area 2 form B , I ν Σ . be convex so that the warp factor can Σ ∗ 0 (8.6) 0 (8.3) B ∗ I T M ) > = b π . In particular, these conditions prevent the ) ) 2 σ D 0 to have constant area is, using an overdot to χ 0 (8.2) a e d ( ( 0 ( = B ∗ E = D 0 i det φ µ e ¨ σ 7 0 B for , Σ = E ∗ 0 is normal to ∗ 0 = B D e = Σ ˙ > σ µν B ∗ = of ) ∗ g σ into spacetime 0 I χ d ( B = 0 De E i Tr 0 ab E χ i therorema egregium , so that it is also necessary that B ]. We will show that the proposed gravity regulator is generic in I 9 0, or 0 = E ˙ σ L the embedding of φ we will have ]. With a regulator, it may become like QCD, with gravitationally free strings confined is, with 9 B B is the volume 3-form of Σ has positive curvature by the For nucleation to begin at The critical acceleration condition is now This adiabatic (constant area) condition may be expressed as follows: Let The basic proposal is that the acceleration of convex surfaces with locally constant area is lim- This effect would limit the strength of gravity, preventing the formation of black holes, which I within this requires nucleation process from occurring in free space, and nucleation is restricted to the environment of where increase as nucleation progresses. In terms of the extrinsic curvature of and denote the Lie derivative so that on and the condition at the initial boundary by Cartan’s magic formula. vector field be a Killing vectorσ and be tangent to the boundary hypersurface 8. Gravity Regulator proposal ited by the Hagedorn Rindler acceleration.of the Note tidal that Riemannian this curvature. condition is not related to the magnitude spacetime dimension, and potentiallydoxes avoids in black types hole of string formation theory. and related information para- would be a novel macroscopic effect. Stringregulator theory [ in 4 dimensions is problematic without a gravity String condensation: Nemesis of Black Holes? to a bag of a different phase [ PoS(PLANCK 2015)057 ] that the M. Hewitt 9 . Deceleration m and ] and increases during M for initial formation and 10 M for the initial formation, and ∼ γ M log 3 − d M ∼ between objects of mass 8 Mm √ ]. The critical surface conditions are a string regularised ∼ is the distance from the existing boundary. This gives es- 10 d (the string tension) throughout relative to local static frames. This is T ∼ ]. This equivalence is universal in that it applies for any uncompactified spacetime di- 9 for particle absorption, where A thermalon shell region is stable on the outside, unstable/dynamic on the inside. Assume Relativistic factors for infalling matter can be estimated as Heuristically the critical gravity condition for conversion is equivalent to the condition that the Similarly to the Newtonian force limit, the conversion power, the rate at which the kinetic Note the generic nature of the conditions, which may apply across M space as the differential d ∼ that thermalon polarization maintainsTransition gravitational would regulation begin at throughout a gravitational separation collapse. 9. Transition process decelerating body generates thermalons inemitted a by way an analogous accelerated charge to during the the Larmor conversion process formula . for the power conversion from the point of viewway, of the an conversion process observer would with be access on only the to same footing the as short any string other sector. dissipative physical In process. this γ timates for transition times (as seen from infinity): Newtonian gravity (in local centre oftension mass [ frame) between any two objects is limited by the string energy of an infalling body isto converted the to string string tension condensate, in any would spacetime take dimension. a This universal is value consistent related with the conjecture [ version of a Penrose trappedHorizons surface are (which is defined the globally infinitethese but string geometric trapped tension conditions. surfaces limit for (and these thermalon surfaces). traps) are defined locally by mension. The mutual nature ofbodies the is proposed shown novel by gravito-thermal the effect symmetrytor, between of which two may the interacting hold Newtonian throughout effective criterion M for space. the gravitational regula- may couple matter to thermalonkinetic production energy to to thermalons, give in asion a stringy power dynamic bremsstrahlung is aspect process, constant of converting the gravito-thermal interaction. The conver- consistent with conversion being a gravitycome sector thermodynamically effect. favoured Note over continued that free conversion fall willconversion once very the process quickly geometric is be- criteria dissipated are met. and can The recording medium be which tracked can through capture the time. informationmodel carried The by arises string the from condensate initial state. entanglement acts The as between entropy a short in this and long string sectors [ geometry applies in all uncompactified dimensionsdifferent string and types, a although self-supporting the condensate mechanism isthe for known heterotic self-dual for strings nature was of conjectured the on the thermalon basis [ of String condensation: Nemesis of Black Holes? collapsed or collapsing objects. PoS(PLANCK 2015)057 ) g 0 in = = T π M. Hewitt αβ T ], and would constitute ’deep firewalls’ 9 9 ]. 8 for particle absorption. Mm √ log 3 − d This model may resolve the ‘firewall paradoxes’ by removing the horizon, and providing a The final state in this scenario is in thermal equilibrium with the exterior normal vacuum (up Consider next a thermalon front geometry with a salient. Could this be produced by a ther- Is conversion to string condensate from Minkowski space possible? Suppose a planar ther- M physically motivated firewall to store thehere information content would of be a formed collapsing by object.be string The bremsstrahlung stable ‘firewall’ during - gravitational there collapse.else is The for no firewall the would black energy hole,condensation, and string and information models the to may have interior go aof except space vacuum gravity. polarization outward has The mechanism by criterion which been for limits Hawking crushed this the evaporation.the to strength so magnitude be there Because effective of is of is the based on tidal nowhere occur the Riemannian at, area curvature. of and accelerating only According surfaces, at, to notholograms, on our sites rather conjecture, than of black this extreme holes. effect gravitationalfirewalls This would collapse. would would be resolve Collapsing real, the objects but firewall black would paradox holes form in would hot the not. following way: the exterior space. In general, theby surface temperature coincidence and and gravity the would object only would matchstably be (i.e. meets unstable. this 2 A matching condition thermalon for deformationof temperature however high and naturally static surface and gravitational gravity acceleration. as it Theinterior is collapsed tied region object to has is the stable undergone location against a collapselapse radial because into, collapse the because and of there their essentially ishot 2 holograms nowhere dimensional formed left from nature, for the these the collapsing finalin matter hot states content the can string [ terminology be to of thought col- [ of as 11. Resolution of paradoxes? 10. Hot holograms to a slow escape of radiationperature equivalent to and the surface Hawking gravity process). can A be hot in object thermal with matching equilibrium tem- with normal vacuum, with malon trap absorbing a particleregion in in Minkowski a space? Minkowski An background,The expanding area which wave-front of bounds is the a inconsistent trailing convex surface withalthough cannot it decrease traps as having associated this a is with locally flatthey Rindler and constant cannot already frames gain area. has energy are minimum by to area. recruiting Thus, be particles that found they everywhere encounter. in Minkowski space, malon trap crosses a wallto of a matter thermalon in excitation Minkowski because space. ofexpectation the that The warp this wall factor process of that should matter be would forbidden be cannot by produced. be the converted This conservation agrees of with energy. the String condensation: Nemesis of Black Holes? ∼ PoS(PLANCK 2015)057 , , M. Hewitt , Journal of , Nuclear Physics , Nuovo Cimento , arxiv:1309.7578 , arXiv:hep-th/9309145 , Springer, Heidelberg (1995). , arXiv:1411.7195, (2014). ,Phys. Rev. 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M.H. wishes to thank George Leontaris for his kind invitation to present this work in Ioannina, [5] O. Lunin and S.D. Mathur, [3] A. Almheiri, D. Marolf, J.Polchinski and J. Sully, [4] L. Braunstein, [6] L. Susskind, [7] M. Hewitt, [9] M.Hewitt, [2] L. Susskind, [8] S.L. Braunstein and S.Pirandola [1] R.B. Mann, [13] J. J. Atick and E. Witten, [15] K.H. O’Brien and C.I. Tan, [12] R. Hagedorn, [14] B. Sathiapalan, [16] T.G.Mertens, H.Verschelde and V.I.Zakharov [10] M. Hewitt, [11] T.G.Mertens, H.Verschelde and V.I.Zakharov [17] T.G.Mertens, H.Verschelde and V.I.Zakharov and Nick Mavromatos for his encouragement. References String condensation: Nemesis of Black Holes? 12. Acknowledgements