×

Obstruction of black hole singularity by quantum field theory effects. (English) Zbl 1388.83361

Summary: We consider the back reaction of the energy due to quantum fluctuation of the background fields considering the trace anomaly for Schwarzschild black hole. It is shown that it will result in modification of the horizon and also formation of an inner horizon. We show that the process of collapse of a thin shell stops before formation of the singularity at a radius slightly smaller than the inner horizon at the order of \(({c}_A\frac{M}{M_p})^{1/3}{l}_p \). After the collapse stops the reverse process takes place. Thus we demonstrate that without turning on quantum gravity and just through the effects the coupling of field to gravity as trace anomaly of quantum fluctuations the formation of the singularity through collapse is obstructed. An important consequence of our work is existence of an extremal solution with zero temperature and a mass which is lower bound for the Schwazschild solution. This solution is also the asymptotic final stable state after Hawking radiation.

MSC:

83C57 Black holes
83C47 Methods of quantum field theory in general relativity and gravitational theory

References:

[1] A. Paranjape and T. Padmanabhan, Radiation from collapsing shells, semiclassical backreaction and black hole formation, Phys. Rev.D 80 (2009) 044011 [arXiv:0906.1768] [INSPIRE].
[2] V.P. Frolov, Do black holes exist?, arXiv:1411.6981 [INSPIRE].
[3] J.M. Bardeen, Black hole evaporation without an event horizon, arXiv:1406.4098 [INSPIRE].
[4] J. Abedi and H. Arfaei, Fermionic greybody factors in dilaton black holes, Class. Quant. Grav.31 (2014) 195005 [arXiv:1308.1877] [INSPIRE]. · Zbl 1304.83027 · doi:10.1088/0264-9381/31/19/195005
[5] A. Ashtekar, T. Pawlowski and P. Singh, Quantum nature of the big bang, Phys. Rev. Lett.96 (2006) 141301 [gr-qc/0602086] [INSPIRE]. · Zbl 1153.83417 · doi:10.1103/PhysRevLett.96.141301
[6] C. Bambi, D. Malafarina and L. Modesto, Terminating black holes in asymptotically free quantum gravity, Eur. Phys. J.C 74 (2014) 2767 [arXiv:1306.1668] [INSPIRE]. · doi:10.1140/epjc/s10052-014-2767-9
[7] C. Bambi, D. Malafarina and L. Modesto, Non-singular quantum-inspired gravitational collapse, Phys. Rev.D 88 (2013) 044009 [arXiv:1305.4790] [INSPIRE].
[8] C. Rovelli and F. Vidotto, Planck stars, Int. J. Mod. Phys.D 23 (2014) 1442026 [arXiv:1401.6562] [INSPIRE]. · doi:10.1142/S0218271814420267
[9] L. Mersini-Houghton, Backreaction of Hawking radiation on a gravitationally collapsing star I: black holes?, Phys. Lett.B 738 (2014) 61 [arXiv:1406.1525] [INSPIRE]. · doi:10.1016/j.physletb.2014.09.018
[10] L. Mersini-Houghton and H.P. Pfeiffer, Back-reaction of the Hawking radiation flux on a gravitationally collapsing star II, arXiv:1409.1837 [INSPIRE].
[11] L. Modesto, Disappearance of black hole singularity in quantum gravity, Phys. Rev.D 70 (2004) 124009 [gr-qc/0407097] [INSPIRE].
[12] R. Torres, Singularity-free gravitational collapse and asymptotic safety, Phys. Lett.B 733 (2014) 21 [arXiv:1404.7655] [INSPIRE]. · Zbl 1370.85003 · doi:10.1016/j.physletb.2014.04.010
[13] R. Torres and F. Fayos, On the quantum corrected gravitational collapse, Phys. Lett.B 747 (2015) 245 [arXiv:1503.07407] [INSPIRE]. · Zbl 1369.85007 · doi:10.1016/j.physletb.2015.05.078
[14] S. Chakraborty, S. Singh and T. Padmanabhan, A quantum peek inside the black hole event horizon, JHEP06 (2015) 192 [arXiv:1503.01774] [INSPIRE]. · Zbl 1388.83408 · doi:10.1007/JHEP06(2015)192
[15] T. Taves and G. Kunstatter, Modelling the evaporation of nonsingular black holes, Phys. Rev.D 90 (2014) 124062 [arXiv:1408.1444] [INSPIRE].
[16] C. Vaz, Quantum gravitational dust collapse does not result in a black hole, Nucl. Phys.B 891 (2015) 558 [arXiv:1407.3823] [INSPIRE]. · Zbl 1328.83067 · doi:10.1016/j.nuclphysb.2014.12.021
[17] H. Culetu, On the Vaz no horizon black hole, arXiv:1407.7119 [INSPIRE]. · Zbl 1170.83407
[18] S.A. Hayward, Formation and evaporation of regular black holes, Phys. Rev. Lett.96 (2006) 031103 [gr-qc/0506126] [INSPIRE]. · doi:10.1103/PhysRevLett.96.031103
[19] H. Kawai, Y. Matsuo and Y. Yokokura, A self-consistent model of the black hole evaporation, Int. J. Mod. Phys.A 28 (2013) 1350050 [arXiv:1302.4733] [INSPIRE]. · Zbl 1380.83149 · doi:10.1142/S0217751X13500504
[20] H. Kawai and Y. Yokokura, Phenomenological description of the interior of the Schwarzschild black hole, Int. J. Mod. Phys.A 30 (2015) 1550091 [arXiv:1409.5784] [INSPIRE]. · Zbl 1325.83018 · doi:10.1142/S0217751X15500918
[21] C. Barceló, R. Carballo-Rubio and L.J. Garay, Mutiny at the white-hole district, Int. J. Mod. Phys.D 23 (2014) 1442022 [arXiv:1407.1391] [INSPIRE]. · doi:10.1142/S021827181442022X
[22] C. Barcelo, R. Carballo-Rubio, L.J. Garay and G. Jannes, The lifetime problem of evaporating black holes: mutiny or resignation, Class. Quant. Grav.32 (2015) 035012 [arXiv:1409.1501] [INSPIRE]. · Zbl 1312.83023 · doi:10.1088/0264-9381/32/3/035012
[23] V.P. Frolov, Mass-gap for black hole formation in higher derivative and ghost free gravity, Phys. Rev. Lett.115 (2015) 051102 [arXiv:1505.00492] [INSPIRE]. · doi:10.1103/PhysRevLett.115.051102
[24] V.P. Frolov, A. Zelnikov and T. de Paula Netto, Spherical collapse of small masses in the ghost-free gravity, JHEP06 (2015) 107 [arXiv:1504.00412] [INSPIRE]. · Zbl 1387.83025 · doi:10.1007/JHEP06(2015)107
[25] L. Modesto and L. Rachwal, Super-renormalizable and finite gravitational theories, Nucl. Phys.B 889 (2014) 228 [arXiv:1407.8036] [INSPIRE]. · Zbl 1326.83061 · doi:10.1016/j.nuclphysb.2014.10.015
[26] L. Modesto, Super-renormalizable quantum gravity, Phys. Rev.D 86 (2012) 044005 [arXiv:1107.2403] [INSPIRE].
[27] A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black holes: complementarity or firewalls?, JHEP02 (2013) 062 [arXiv:1207.3123] [INSPIRE]. · Zbl 1342.83121 · doi:10.1007/JHEP02(2013)062
[28] S.L. Braunstein, S. Pirandola and K. Życzkowski, Better late than never: information retrieval from black holes, Phys. Rev. Lett.110 (2013) 101301 [arXiv:0907.1190] [INSPIRE]. · doi:10.1103/PhysRevLett.110.101301
[29] S.B. Giddings and W.M. Nelson, Quantum emission from two-dimensional black holes, Phys. Rev.D 46 (1992) 2486 [hep-th/9204072] [INSPIRE].
[30] D.N. Page, Information in black hole radiation, Phys. Rev. Lett.71 (1993) 3743 [hep-th/9306083] [INSPIRE]. · Zbl 0972.83567 · doi:10.1103/PhysRevLett.71.3743
[31] S. Hossenfelder and L. Smolin, Conservative solutions to the black hole information problem, Phys. Rev.D 81 (2010) 064009 [arXiv:0901.3156] [INSPIRE].
[32] S.B. Giddings, Black holes and massive remnants, Phys. Rev.D 46 (1992) 1347 [hep-th/9203059] [INSPIRE].
[33] E. Poisson and W. Israel, Structure of the black hole nucleus, Class. Quant. Grav.5 (1988) L201 [INSPIRE]. · doi:10.1088/0264-9381/5/12/002
[34] W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cim.B 44 (1966) 1. · doi:10.1007/BF02710419
[35] K. Kuchar, Charged shells in general relativity and their gravitational collapse, Czech. J. Phys.B 18 (1968) 435. · doi:10.1007/BF01698208
[36] S.B. Giddings and A. Nudelman, Gravitational collapse and its boundary description in AdS, JHEP02 (2002) 003 [hep-th/0112099] [INSPIRE]. · doi:10.1088/1126-6708/2002/02/003
[37] E. Poisson, A relativist’s toolkit: the Mathematics of black-hole mechanics, Cambridge University Press, Camrbidge U.K. (2004). · Zbl 1058.83002 · doi:10.1017/CBO9780511606601
[38] M.R. Brown, A.C. Ottewill and D.N. Page, Conformally invariant quantum field theory in static Einstein space-times, Phys. Rev.D 33 (1986) 2840 [INSPIRE].
[39] D.M. Capper and M.J. Duff, Trace anomalies in dimensional regularization, Nuovo Cim.A 23 (1974) 173. · doi:10.1007/BF02748300
[40] S. Deser, M.J. Duff and C.J. Isham, Nonlocal conformal anomalies, Nucl. Phys.B 111 (1976) 45 [INSPIRE]. · Zbl 0967.81529 · doi:10.1016/0550-3213(76)90480-6
[41] M.J. Duff, Observations on conformal anomalies, Nucl. Phys.B 125 (1977) 334 [INSPIRE]. · doi:10.1016/0550-3213(77)90410-2
[42] M.J. Duff, Twenty years of the Weyl anomaly, Class. Quant. Grav.11 (1994) 1387 [hep-th/9308075] [INSPIRE]. · Zbl 0808.53063 · doi:10.1088/0264-9381/11/6/004
[43] P. Pascual, J. Taron and R. Tarrach, The spin-2 gravitational trace anomaly, Phys. Rev.D 39 (1989) 2993 [INSPIRE].
[44] N.D. Birrell and P.C.W. Davies, Quantum fields in curved space, Cambridge University Press, Cambridge U.K. (1984). · Zbl 0972.81605
[45] E. Mottola, New horizons in gravity: the trace anomaly, dark energy and condensate stars, Acta Phys. Polon.B 41 (2010) 2031 [arXiv:1008.5006] [INSPIRE]. · Zbl 1371.83107
[46] A. Belokogne and A. Folacci, Renormalized stress tensor for massive fields in Kerr-Newman spacetime, Phys. Rev.D 90 (2014) 044045 [arXiv:1404.7422] [INSPIRE].
[47] V.P. Frolov and A.I. Zelnikov, Vacuum polarization of massive fields near rotating black holes, Phys. Rev.D 29 (1984) 1057 [INSPIRE].
[48] S.M. Christensen and S.A. Fulling, Trace anomalies and the Hawking effect, Phys. Rev.D 15 (1977) 2088 [INSPIRE].
[49] I.L. Shapiro, Effective action of vacuum: semiclassical approach, Class. Quant. Grav.25 (2008) 103001 [arXiv:0801.0216] [INSPIRE]. · Zbl 1140.83301 · doi:10.1088/0264-9381/25/10/103001
[50] R. Balbinot, A. Fabbri and I.L. Shapiro, Vacuum polarization in Schwarzschild space-time by anomaly induced effective actions, Nucl. Phys.B 559 (1999) 301 [hep-th/9904162] [INSPIRE]. · Zbl 0957.81012 · doi:10.1016/S0550-3213(99)00424-1
[51] R. Balbinot, A. Fabbri and I.L. Shapiro, Anomaly induced effective actions and Hawking radiation, Phys. Rev. Lett.83 (1999) 1494 [hep-th/9904074] [INSPIRE]. · Zbl 0957.81012 · doi:10.1103/PhysRevLett.83.1494
[52] E. Elizalde, S. Nojiri and S.D. Odintsov, Possible quantum instability of primordial black holes, Phys. Rev.D 59 (1999) 061501 [hep-th/9901026] [INSPIRE].
[53] A.A. Bytsenko, S. Nojiri and S.D. Odintsov, Quantum generation of Schwarzschild-de Sitter (Nariai) black holes in effective Dilaton-Maxwell gravity, Phys. Lett.B 443 (1998) 121 [hep-th/9808109] [INSPIRE]. · doi:10.1016/S0370-2693(98)01330-6
[54] S. Nojiri and S.D. Odintsov, Quantum evolution of Schwarzschild-de Sitter (Nariai) black holes, Phys. Rev.D 59 (1999) 044026 [hep-th/9804033] [INSPIRE].
[55] S. Nojiri and S.D. Odintsov, Thermodynamics of Schwarzschild-(Anti-)de Sitter black holes with account of quantum corrections, Int. J. Mod. Phys.A 15 (2000) 989 [hep-th/9905089] [INSPIRE]. · Zbl 1052.83520
[56] R. Casadio and C. Germani, Gravitational collapse and black hole evolution: do holographic black holes eventually ‘anti-evaporate’ ?, Prog. Theor. Phys.114 (2005) 23 [hep-th/0407191] [INSPIRE]. · Zbl 1076.83014 · doi:10.1143/PTP.114.23
[57] R. Casadio and C. Germani, Gravitational collapse and evolution of holographic black holes, J. Phys. Conf. Ser.33 (2006) 434 [hep-th/0512202] [INSPIRE]. · doi:10.1088/1742-6596/33/1/055
[58] S. Singh and S. Chakraborty, Black hole kinematics: The “in”-vacuum energy density and flux for different observers, Phys. Rev.D 90 (2014) 024011 [arXiv:1404.0684] [INSPIRE].
[59] L.H. Ford, Quantum vacuum energy in a closed universe, Phys. Rev.D 14 (1976) 3304 [INSPIRE].
[60] L.H. Ford, Quantum vacuum energy in general relativity, Phys. Rev.D 11 (1975) 3370 [INSPIRE].
[61] J.T. Firouzjaee and G.F.R. Ellis, Cosmic matter flux may turn Hawking radiation off, Gen. Rel. Grav.47 (2015) 6 [arXiv:1408.0778] [INSPIRE]. · Zbl 1329.83108 · doi:10.1007/s10714-014-1848-2
[62] J.T. Firouzjaee and R. Mansouri, Radiation from a dust dynamical LTB black hole, Europhys. Lett.97 (2012) 29002 [arXiv:1104.0530] [INSPIRE]. · doi:10.1209/0295-5075/97/29002
[63] R. Brout, S. Massar, R. Parentani and P. Spindel, A primer for black hole quantum physics, Phys. Rept.260 (1995) 329 [arXiv:0710.4345] [INSPIRE]. · doi:10.1016/0370-1573(95)00008-5
[64] L. Parker, Aspects of quantum field theory in curved space-time: effective action and energy-momentum tensor, in Recent developments in gravitation, M. Lévy and S. Deser eds., NATO Advanced Study Institutes Series volume 44, Springer (1979).
[65] S.M. Christensen and M.J. Duff, Axial and conformal anomalies for arbitrary spin in gravity and supergravity, Phys. Lett.B 76 (1978) 571 [INSPIRE]. · doi:10.1016/0370-2693(78)90857-2
[66] I. Dymnikova, Cosmological term as a source of mass, Class. Quant. Grav.19 (2002) 725 [gr-qc/0112052] [INSPIRE]. · Zbl 1005.83051 · doi:10.1088/0264-9381/19/4/306
[67] I. Dymnikova, Spherically symmetric space-time with the regular de Sitter center, Int. J. Mod. Phys.D 12 (2003) 1015 [gr-qc/0304110] [INSPIRE]. · Zbl 1079.83507 · doi:10.1142/S021827180300358X
[68] G.T. Horowitz and S.F. Ross, Naked black holes, Phys. Rev.D 56 (1997) 2180 [hep-th/9704058] [INSPIRE].
[69] S. Ansoldi, Spherical black holes with regular center: a review of existing models including a recent realization with Gaussian sources, arXiv:0802.0330 [INSPIRE].
[70] S. Carroll, Spacetime and geometry: an introduction to general relativity, Benjamin Cummings (2003).
[71] S. Antoci and D.E. Liebscher, Reconsidering Schwarzschild’s original solution, Astron. Nachr.322 (2001) 137 [gr-qc/0102084] [INSPIRE]. · Zbl 0994.83034 · doi:10.1002/1521-3994(200107)322:3<137::AID-ASNA137>3.0.CO;2-1
[72] J. Plebanski and A. Krasinski, An introduction to general relativity and cosmology, Cambridge University Press, Cambridge U.K. (2006). · Zbl 1103.83001 · doi:10.1017/CBO9780511617676
[73] A. Bonanno and M. Reuter, Spacetime structure of an evaporating black hole in quantum gravity, Phys. Rev.D 73 (2006) 083005 [hep-th/0602159] [INSPIRE].
[74] Y.S. Myung, Y.-W. Kim and Y.-J. Park, Thermodynamics and evaporation of the noncommutative black hole, JHEP02 (2007) 012 [gr-qc/0611130] [INSPIRE]. · doi:10.1088/1126-6708/2007/02/012
[75] S. Hossenfelder, L. Modesto and I. Premont-Schwarz, A model for non-singular black hole collapse and evaporation, Phys. Rev.D 81 (2010) 044036 [arXiv:0912.1823] [INSPIRE].
[76] E. Alesci and L. Modesto, Particle creation by loop black holes, Gen. Rel. Grav.46 (2014) 1656 [arXiv:1101.5792] [INSPIRE]. · Zbl 1286.83039 · doi:10.1007/s10714-013-1656-0
[77] P. Chen, Y.C. Ong and D.-h. Yeom, Black hole remnants and the information loss paradox, Phys. Rept.603 (2015) 1 [arXiv:1412.8366] [INSPIRE]. · doi:10.1016/j.physrep.2015.10.007
[78] T. De Lorenzo, C. Pacilio, C. Rovelli and S. Speziale, On the effective metric of a Planck star, Gen. Rel. Grav.47 (2015) 41 [arXiv:1412.6015] [INSPIRE]. · Zbl 1317.83034 · doi:10.1007/s10714-015-1882-8
[79] A. Barrau and C. Rovelli, Planck star phenomenology, Phys. Lett.B 739 (2014) 405 [arXiv:1404.5821] [INSPIRE]. · doi:10.1016/j.physletb.2014.11.020
[80] W. Israel, Gravitational collapse and causality, Phys. Rev.153 (1967) 1388 [INSPIRE]. · doi:10.1103/PhysRev.153.1388
[81] A. Ashtekar and M. Bojowald, Quantum geometry and the Schwarzschild singularity, Class. Quant. Grav.23 (2006) 391 [gr-qc/0509075] [INSPIRE]. · Zbl 1090.83021 · doi:10.1088/0264-9381/23/2/008
[82] L. Modesto, Loop quantum black hole, Class. Quant. Grav.23 (2006) 5587 [gr-qc/0509078] [INSPIRE]. · Zbl 1101.83033 · doi:10.1088/0264-9381/23/18/006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.