PoS(FFP14)038 http://pos.sissa.it/ ∗ Fluctuations in the horizon that naturally arise in the quantum space time allow radiation [email protected] [email protected] Speaker. to emerge during theproceed evaporation beyond process Page time due without to reaching theof stimulated maximum the entanglement emission white limit hole. allowing until No the evaporation firewalls formation to nor remnants arise in this scenario. We incorporate elements of the recently discoveredloop exact quantum solutions gravity of for the vacuum quantum spherically constraintshole symmetric of evaporation space-times due into to the Ashtekar paradigm andsymmetry of of Bojowald. the black solutions The implies quantization that the of numberis the of nice finite. area slices that of The can the foliation be fit eventually surfaces inside moves of theory the through black used the hole region to where be theemerge singularity and in finally all the as classical the a white particleset hole. that al. This fell yields into a the variant black of a hole scenario due advocated to by Arkani-Hamed Hawking radiation ∗ Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c

Frontiers of Fundamental Physics 14 -15-18 FFP14, July 2014 Aix Marseille University (AMU) Saint-Charles Campus, Marseille Rodolfo Gambini Instituto de Física, Facultad de Ciencias,E-mail: Montevideo, Uruguay Jorge Pullin A scenario for black hole evaporationgeometry on a quantum Department of Physics and Astronomy, LouisianaE-mail: State University, Baton Rouge, LA 70803 PoS(FFP14)038 ], the 5 Jorge Pullin 1 dimensional model [ + ]. This was due to the realization that 1 2 0 and eventually becomes time-like, ending up by = r ] and of results in CGHS 1 4 ]. The three principles of black hole complementarity are: 1) That the 6 ]. Motivated by loop quantum gravity analyses of the black hole interior treating 3 The Penrose diagram of the Ashtekar–Bojowald paradigm. As matter collapses, a trapping horizon We would like to argue that when one incorporates elements of the new exact solution, namely, In a recent development, the exact space of solutions of the equations of loop quantum gravity A paradigm for black hole evaporation in loop quantum gravity was put forward by Ashtekar touching the region where a semiclassical space-time description is not available. the spatial discreteness implied by the quantizationstates of are area in superpositions loop quantum with gravity different andpicture the masses emerges fact and that that spin introduces networks, smallhole to but complementarity the significant [ above modifications paradigm, to a Susskind’s new notion of black picture that emerges is thehorizon one depicted forms, in initially 1. space-like As near a star collapses to form a black hole, a trapping forms, initially spatial and eventually timelike.cal The space-time shaded and region is is where not the well classical approximated singularity by was. a semiclassi- Figure 1: it as a Kantowski–Sachs cosmology [ for vacuum, spherically symmetric space-times was found [ and Bojowald [ Scenario for black hole evaporation a rescaling and linear combination ofcase the yields constraints a constraint of algebra canonical that quantum isprocedure gravity a in for Lie the algebra. the spherical This model. allows toIt complete Remarkably, is the the Dirac based space quantization on of onebounded physical dimensional below spin states by networks. can the be The condition proximity foundsingularity of of in the that the closed quantization is nodes of form. inside of the the blacka areas spin holes description of networks in in the is terms spheres classical of of generalanother a symmetry. relativity region semiclassical The is of geometry replaced space-time. is by notblack Although a possible hole, this region and elements solution where through corresponds from it to itsoration one an description scenarios. tunnels eternal can into time Concretely, be independent there heuristicallybe are incorporated extended two into to black lessons the hole from evaporatinghole evap- the case: interior eternal is a) black finite The holesecond due number model lesson to of that is the nice that can quantization slices themass) of that Dirac undergoes areas can fluctuations observable present that be associated grow in with fit withimplications the the time. into for quantum position We the the will space-time; of resulting black see scenario. the b) these horizon elements the can (the have ADM interesting PoS(FFP14)038 Jorge Pullin in ordinary Schwarzschild . const = r ]. These points remain unchanged 7 and inside to . 3 const slices in the interior (in Schwarzschild coordinates). . = t const = r slices in the exterior to The “nice slices” that enter the black hole and whose stretching is responsible for the Hawking . ]. These are spatial slices of the space-time that penetrate the horizon interpolating between A standard way to describe Hawking radiation is to consider the construction of “nice slices” One of the new elements introduced by the quantum space-time of loop quantum gravity is const 9 , r=0 r=2M = 8 Figure 2: radiation. Outside they asymptote to surfaces This requires a stretching in theon region one around the slice horizon. is The notaccounts stretching the implies for vacuum that the the on Hawking vacuum radiation. futurea slices Each particle and particle emitted this inside in implies the the creation blackthermal, exterior since of hole. becomes part pairs entangled of of the For with information particles an isof and lost, observer freedom at not in least accessible locally, the and behind one asymptotic thethe needs region, horizon. to exterior trace the The over of slices the radiation the degrees are appears usuallythe black constructed radiation hole with produced of a has spacing the the in energyHawking order radiation. corresponding of to twice the maximum the of Schwarzschild the radius. standard spectrum This of ensures that [ that the separation of the slicesspheres is of bounded spherical below symmetry. by theexact The rule solution background of for quantum the the space-time quantization physical that of space the emerges of area from states of the in the new spherical symmetry is based on one dimensional Scenario for black hole evaporation evolution is unitary, there isradiation. an This S is matrix unmodified. describingtheory the 2) evolution Outside on of the a horizon, infalling classical physics mattercase background can to the with be Hawking background described small is by but quantum representedon important field by suitable quantum a quantum gravity geometry states corrections. given thatimply by fluctuations approximate In in the the the our expectation classical position values behavior. ofdepartures of the from The horizon the quantum that quantum metric field play gravity theory an effects 3) in important To role curved a in space distant providing time important observer at athe times black purposes of hole of the appears entropy order as calculations. ofas a the In we quantum Page our will system time. case, note with this later. discretedoes is In energy not implied levels addition by notice for it the anything is quantization unusual usuallyin of when assumed our the crossing that analysis. areas, the an horizon observer [ falling into the black hole coordinates. t PoS(FFP14)038 , ) 4 ¯ hGc ( / 3 that are M k 3 ~ Jorge Pullin G ]. Therefore 11 . This gives 16 c / ) GM 4 )( that can be assigned to the black hole k ~ . Although we have based our discussion 2 Planck ) /` 2 ) 2 Planck 4 /` GM 2 2 ) (( GM 2 ]. This work is currently being extended to self gravitating (( at the various links of the spin network. This implies that for 10 . Elsewhere, the separation of the slices is bounded below by k on which the network is based and a set of integers g Planck 2 Planck ` ` π 0 has to be eliminated in order to have a self-adjoint metric operator and ). Its logarithm then yields an entropy proportional to the area in Planck = M k ] we discuss the collapse of test shells and in a manuscript in preparation we extend (this is the number of all possible vectors 10 . The value ]. It would also imply that the scenario we are proposing could not take place. This ) 7 r 2 Planck 2 ( /` 2 / ) An objection that could be raised to this scenario is that as the black hole evaporates, it is well Remarkably, this simple one dimensional model of black hole reproduces correctly the en- In turn, this means that from the point of view of an observer far away from the black hole, the After the slices cross the region where the classical singularity used to be and become more GM 2 ( 2 Planck know that the interior becomesare more not and enough degrees more of entangled freedom with left the in outgoing the radiation interior until to continue there the evaporation [ shells. Once the nice slicestheir went discussion through requires that a full region, quantum they treatment. have it in their past and therefore even Hawking evaporation should stop inshould a work very regime well. where quantumproblem This, field [ among theory other in reasons, curved led space to time the proposal of firewalls to avoid this the results to self-gravitating shells. tropy calculation. If2 one considers all possible states in the interior, its number is bounded by Scenario for black hole evaporation spin networks. One hasthe a valences graph the edges ofcan the take spin on network. these states The arethe 4 values slices that the in areas the of interiorthe the of radial spheres the coordinate of black of symmetry hole order ` that are close to the singularity one has a separation in interior for a given mass units with a factor of order unity. traditional evaporation process lasts a time Int that implies that the singularity presentapproach. in the This classical in Schwarzschild turn solution means isnumber eliminated that of in in slices this the bounded interior above by of Int the black hole can only accommodate a finite on a model of eternal blackobservables hole is in available loop in quantum models gravity, that a involve similarIn collapse, description reference as with [ can the be same illustrated Dirac with collapsing shells. and more like ordinary slices of Minkowskithe space, particles the usual that Hawking fell evaporation switchesprecise into off picture and the of black how hole the radiationdetail. are that That allowed emerges would to after require studying the emerge. how traditional thewith evaporation particles the At stops that earlier this behaves fell outgoing radiation) into in point interact the we with blackclassical the hole cannot singularity region (and of used are give high entangled to a curvature be. surrounding where Aof the preliminary the relevant study effects of can shells be crossing seen the in region, [ exhibiting some which is of the orderwhere of the magnitude of classical the singularity Page usedgood time. to approximation At be anymore this and time, to quantum the thethe field nice relevant singularity theory slices physics. in was reach curved in the Once space-time region theduring the is the classical not slices evaporation theory, a traverse emerge all the in thean a region order particles white where of that hole. magnitude fell estimate, Notice we inevaporation are that in due ignoring the its several to calculation. previous important Hawking effects, evaporation including time radiation the is black only hole PoS(FFP14)038 . ) 2 / Planck 3 ` ( O Jorge Pullin + ] this is taken 1 Planck ` ]. A heuristic picture GM . The horizon therefore 13 c 2 / √ 2 GM = dr 1 − r / S r − 1 p 5 Planck ` + S S r ]. In their original proposal the limitation was given by r R 9 ] but they would require certain modifications of how one treats the matter 15 ]. The large differences in characteristic frequencies associated with the positions 12 This mechanism of finite number of nice slices therefore provides a variant of an implementa- Since in our approach there is no singularity, the particles of the Hawking radiation that fell ] as a solution of the information problem by itself, however it does not appear be a strong 14 Hamiltonian, that exceed the scopeeffect of of this spontaneous note. and stimulated So emission athole will is this allow formed point the but we evaporation this conjecture to remains continue that to till the be the confirmed. combined white tion of a proposal by Arkani-Hamed et al. [ bounds on the accuracy for measuring timessuch between limitation two arises successive from slices that the wasswitches loop heuristic. quantization off Here of gradually the after space-time theused and to the slices be. traditional make evaporation it through the region where the classical singularity enough effect to account for thedoes exit not of face all this the problem informationwhite as at hole the the (plus information end the can of effect further the leadingfail exit to process. to in be stimulated Our perfectly significant thermal emission scenario quantities due appears to through stimulatedtemperature. larger). the emission. Hawking The This radiation will radiation manifest will itself may into also fluctuations in the exhibit the a stimulated certain emission, degree absentgrows of in at coherence ordinary a or Hawking smaller non-thermality radiation. ratecould due than be In the calculated other one in words, predicted detailtime entanglement by and techniques ordinary the of magnitude Hawking [ of radiation. this These effect deviations estimated with the quantum space- into account since the massthe of generic the black solution hole representing is awith a classical different Dirac space values observable of time with the will continuous mass,state be spectrum centered near given in and the by a horizon given a will classical superposition fluctuate value.time of from That a states being means particle a that of vacuum the the into quantum Hawkingamount having radiation given particles. by is the Specifically, emitted, time-energy every the uncertainty mass relation.by of the The the separation characteristic of time black the for hole “nice emission will slices” is fluctuate and given by is therefore an of the order of 2 So it is a cumulativeproduction effect [ on the position of the horizon due to the back-reaction of the particle of the horizon in the fluctuationvacuum —due in to one the high position blueshifts willlead close be to to stimulated the significantly horizon—, emission different imply in thanother that the the types the Hawking of vacuum radiation fluctuations in of of the similar the other. nature horizon in to This black that would hole due analogue to systems thermal [ and Scenario for black hole evaporation point of view doeshave not fluctuations take of into the position account of that the horizon. in a In the situation exact with solution presented a in quantum [ geometry, one will carries out a “random walk”the in order of position the and Planck after mass.extrema a This of the Page implies fluctuations a time of separation the the in order fluctuation of the 2 in distance between its the position inner is and of outer is that a particle createdthe by same pair production quantum for numbers a forto horizon a quantum will horizon effects. stimulate further emission This out of extra asentanglement particles emission the entropy with allows position as the of black the the hole outgoingwith horizon to particle any fluctuates lose generated infalling due mass by particle. without stimulated increasing[ Stimulated emission the emission is (with not a entangled very different origin) has been proposed PoS(FFP14)038 ] and 7 Jorge Pullin ] in that there is a region 17 6 ]: “To an external observer a white hole is indistinguishable 16 The proposed paradigm. A trapping horizon forms during the Hawking radiation period. When the Notice that we have respected complementarity, there was no need to invoke firewalls [ As the picture that emerges is that of a white hole, it suggests that no “remnant” is produced, the information is naturally retrieveda completely scenario without where remnants. quantum field However, theory although in we curved have spacetime applies locally in the regions of low of space-time that is in causal contactdescription with and a that region is where the one source needsphase, of the it full the is quantum asymmetry theory unlikely in for to the its against radiation. have white a In holes purely particular that in thermal argue the they spectrum.the white are space-time, hole Notice unstable which are that in based the some on Ashtekar-Bojowald of picture the the do existence arguments not of emerge. given Cauchy horizons for although the true details will dependmoment on we the do dynamics not in have. theThe Asymptotically, region the information of information of high could the curvature therefore which potentially firstthe at be usual particle the retrieved. Hawking of radiation each (and the producedfell stimulated pair into emission) could the and black be the hole information retrievedproposal of is at is the radiated infinity to particle to through start that infinity withthat in a emerge through black the the hole white white hole that hole hadradiation morphs phase. complicated of interactions into in the What a the white we white region hole of hole. arehas high is doing some curvature, not However, the similarities in since the with our the the same model particles as considered the by Parikh one and produced Wilczek [ during the black hole phase. This from a black hole. TheThe process irreversibility of which hole arises in formation theconsidering and there classical evaporation is is limit no completely is reason time-symmetric. just for a the statistical process effect”. to be In time-symmetric, the though. case we are Figure 3: into the black hole canThe in detailed principle description traverse of the that regioninformation that traversing where fell is the into classical involved, the black but singularity holeused in used not to principle to to be. get be. there The out resulting is by picture traversingwhite no is the hole reason region that where proposal of for the a of the singularity white Hawking hole, [ with considerable similarity to the original radiation ends one has athe white process hole of that generation radiates of the Hawkingof information radiation the that and Hawking had no radiation fallen outgoing remnant into and is the infalling left trapping into behind. horizon the The in black arrows hole indicate and particles particles of the white hole exiting. Scenario for black hole evaporation PoS(FFP14)038 , 52 Jorge Pullin 977 , 055 (2007) , 018 (2013) 0705 , 044040 (2011) 1309 83 , 104030 (2007) [arXiv:0709.2129 76 , 062 (2013) [arXiv:1207.3123 , 095009 (2014) [arXiv:1310.5996 , 3743 (1993) [hep-th/9306069]. 31 1302 48 , 3349 (2005) [gr-qc/0504029]. , 391 (2006) [gr-qc/0509075]; Böhmer and 22 23 7 , no. 21, 211301 (2013) [arXiv:1302.5265 [gr-qc]]; , 2204 (2007) [gr-qc/0601088]. 46 110 ] and in particular imply the elimination of singularities 15 , 224001 (2009) [arXiv:0909.1038 [hep-th]]. , 2235 (2006) [gr-qc/0411032]; A. Ashtekar, M. Bojowald 26 45 , 028 (2013) [arXiv:1301.4995 [hep-th]]. , 161303 (2011) [arXiv:1011.6442 [gr-qc]]; Phys. Rev. D 1309 106 [arXiv:1304.6483 [hep-th]]; see also S. L.S. Braunstein, L. [arXiv:0907.1190v1 Braunstein, [quant-ph]] S. published Pirandola as andsimilar K. prediction Zyczkowski, from Physical different Review assumptions. Letters 110, 101301 (2013) for a [hep-th]]; A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, JHEP [gr-qc]]; R. Gambini, J. Pullin, M.(2008) Campiglia, [arXiv:0712.0817 R. [gr-qc]]. Gambini and J. Pullin, AIP Conf. Proc. [arXiv:1012.0077 [gr-qc]]. [arXiv:0704.1814 [hep-th]]. Vandersloot C. G. Boehmer and K. Vandersloot, Phys. Rev. D [gr-qc]]. A. Ashtekar and M. Bojowald, Class. Quant. Grav. R. Gambini, J. Olmedo and J. Pullin, Class. Quant. Grav. We wish to thank Don Marolf for many helpful discussions. This work was supported in part [4] L. Modesto, Int. J. Theor. Phys. [2] R. Gambini and J. Pullin, “Quantum[3] shells inA. a Ashtekar quantum and space-time,” arXiv:1408.4635 M. [gr-qc]. Bojowald, Class. Quant. Grav. [1] R. Gambini and J. Pullin, Phys. Rev. Lett. [8] S. D. Mathur, Class. Quant. Grav. [9] N. Arkani-Hamed, S. Dubovsky, A. Nicolis, E. Trincherini and G. Villadoro, JHEP [7] A. Almheiri, D. Marolf, J. Polchinski and J. Sully, JHEP [5] Phys. Rev. Lett. [6] L. Susskind, L. Thorlacius and J. Uglum, Phys. Rev. D [10] R. Gambini, J. Pullin “Collapsing shells[11] in aD. quantum N. space-time”, Page, in JCAP preparation. [12] B. L. Hu and A. Roura, Int. J. Theor. Phys. by grant NSF-PHY-1305000, funds of thePedeciba. 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