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Effective quantum dust collapse via surface matching. (English) Zbl 1482.83094

Summary: The fate of matter forming a black hole is still an open problem, although models of quantum gravity corrected black holes are available. In loop quantum gravity (LQG) models were presented, which resolve the classical singularity in the centre of the black hole by means of a black-to-white hole transition, but neglect the collapse process. The situation is similar in other quantum gravity approaches, where eternal non-singular models are available. In this paper, a strategy is presented to generalise these eternal models to dynamical collapse models by surface matching. Assuming (1) the validity of a static quantum black hole spacetime outside the collapsing matter, (2) homogeneity of the collapsing matter, and (3) differentiability at the surface of the matter fixes the dynamics of the spacetime uniquely. It is argued that these assumptions resemble a collapse of pressure-less dust and thus generalises the Oppenheimer-Snyder-Datt model, although no precise model of the matter has to be assumed. Hawking radiation is systematically neglected in this approach. The junction conditions and the spacetime dynamics are discussed generically for bouncing black hole spacetimes, as proposed by LQG, although the scheme is approach independent. Further, the equations are explicitly solved for the recent model N. Bodendorfer et al. [Classical Quantum Gravity 36, No. 19, Article ID 195015, 46 p. (2019; Zbl 1478.83126)] and a global spacetime picture of the collapse is achieved. The causal structure is discussed in detail and the Penrose diagram is constructed. The trajectory of the collapsing matter is completely constructed from an inside and outside observer point of view. The general analysis shows that the matter is collapsing and re-expanding and crosses the Penrose diagram diagonally. This way the infinite tower of Penrose diagrams, as proposed by several LQG models, is generically not cut out. Questions about different timescales of the collapse for in- and outside observers can be answered.

MSC:

83C57 Black holes
83C45 Quantization of the gravitational field
05D15 Transversal (matching) theory
83C30 Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
83E05 Geometrodynamics and the holographic principle
81T12 Effective quantum field theories

Citations:

Zbl 1478.83126

References:

[1] Bodendorfer, N.; Mele, F. M.; Münch, J., Effective quantum extended spacetime of polymer Schwarzschild black hole, Class. Quantum Grav., 36 (2019) · Zbl 1478.83126 · doi:10.1088/1361-6382/ab3f16
[2] Penrose, R., Gravitational collapse and space-time singularities, Phys. Rev. Lett., 14, 57-59 (1965) · Zbl 0125.21206 · doi:10.1103/physrevlett.14.57
[3] Hawking, S., Properties of expanding universes, PhD Thesis (1966)
[4] Bojowald, M., Singularities and quantum gravity, AIP Conf. Proc., 910, 294-333 · Zbl 1157.83001 · doi:10.1063/1.2752483
[5] Natsuume, M., The singularity problem in string theory (2001)
[6] Ashtekar, A.; Pawlowski, T.; Singh, P., Quantum nature of the big bang: improved dynamics, Phys. Rev. D, 74 (2006) · Zbl 1197.83047 · doi:10.1103/physrevd.74.084003
[7] Ashtekar, A.; Bojowald, M.; Lewandowski, J., Mathematical structure of loop quantum cosmology, Adv. Theor. Math. Phys., 7, 233-268 (2003) · doi:10.4310/atmp.2003.v7.n2.a2
[8] Ashtekar, A.; Pullin, J., Loop Quantum Gravity: The First 30 years (2017), Singapore: World Scientific, Singapore · Zbl 1367.83004
[9] Dapor, A.; Liegener, K., Cosmological effective Hamiltonian from full loop quantum gravity dynamics, Phys. Lett. B, 785, 506-510 (2018) · Zbl 1398.81287 · doi:10.1016/j.physletb.2018.09.005
[10] Bojowald, M., Critical evaluation of common claims in loop quantum cosmology, Universe, 6, 36 (2020) · doi:10.3390/universe6030036
[11] Vakili, B., Classical polymerization of the Schwarzschild metric, Adv. High Energy Phys., 2018, 1-10 (2018) · Zbl 1402.83047 · doi:10.1155/2018/3610543
[12] Corichi, A.; Singh, P., Loop quantization of the Schwarzschild interior revisited, Class. Quantum Gravity, 33 (2015) · Zbl 1336.83021 · doi:10.1088/0264-9381/33/5/055006
[13] Modesto, L., Semiclassical loop quantum black hole, Int. J. Theor. Phys., 49, 1649-1683 (2010) · Zbl 1200.83003 · doi:10.1007/s10773-010-0346-x
[14] Modesto, L.; Prémont-Schwarz, I., Self-dual black holes in loop quantum gravity: theory and phenomenology, Phys. Rev. D, 80 (2009) · doi:10.1103/physrevd.80.064041
[15] Ben Achour, J.; Lamy, F.; Liu, H.; Noui, K., Polymer Schwarzschild black hole: an effective metric, Europhys. Lett., 123 (2018) · doi:10.1209/0295-5075/123/20006
[16] Bojowald, M.; Brahma, S.; Yeom, D-h, Effective line elements and black-hole models in canonical loop quantum gravity, Phys. Rev. D, 98 (2018) · doi:10.1103/physrevd.98.046015
[17] Boehmer, C. G.; Vandersloot, K., Loop quantum dynamics of the Schwarzschild interior, Phys. Rev. D, 76 (2007) · doi:10.1103/physrevd.76.104030
[18] Ashtekar, A.; Olmedo, J.; Singh, P., Quantum extension of the Kruskal spacetime, Phys. Rev. D, 98 (2018) · doi:10.1103/physrevd.98.126003
[19] Ashtekar, A.; Olmedo, J.; Singh, P., Quantum transfiguration of kruskal black holes, Phys. Rev. Lett., 121 (2018) · doi:10.1103/physrevlett.121.241301
[20] Bodendorfer, N.; Mele, F. M.; Münch, J., Mass and horizon Dirac observables in effective models of quantum black-to-white hole transition (2021) · Zbl 1483.83022
[21] Bodendorfer, N.; Mele, F. M.; Münch, J., (b, v)-type variables for black to white hole transitions in effective loop quantum gravity (2019)
[22] Assanioussi, M.; Dapor, A.; Liegener, K., Perspectives on the dynamics in a loop quantum gravity effective description of black hole interiors, Phys. Rev. D, 101 (2019) · doi:10.1103/physrevd.101.026002
[23] Ashtekar, A.; Olmedo, J., Properties of a recent quantum extension of the Kruskal geometry (2020) · Zbl 1443.83020
[24] Bouhmadi-López, M.; Brahma, S.; Chen, C-Y; Chen, P.; Yeom, D-h., Asymptotic non-flatness of an effective black hole model based on loop quantum gravity, Phys. Dark Universe, 30 (2020) · doi:10.1016/j.dark.2020.100701
[25] Kelly, J. G.; Santacruz, R.; Wilson-Ewing, E., Effective loop quantum gravity framework for vacuum spherically symmetric spacetimes, Phys. Rev. D, 102 (2020) · doi:10.1103/physrevd.102.106024
[26] Kelly, J. G.; Santacruz, R.; Wilson-Ewing, E., Black hole collapse and bounce in effective loop quantum gravity, Class. Quantum Grav., 38 (2021) · Zbl 1479.83089 · doi:10.1088/1361-6382/abd3e2
[27] Gambini, R.; Olmedo, J.; Pullin, J., Spherically symmetric loop quantum gravity: analysis of improved dynamics, Class. Quantum Grav., 37 (2020) · Zbl 1479.83084 · doi:10.1088/1361-6382/aba842
[28] Geiller, M.; Livine, E. R.; Sartini, F., Symmetries of the black hole interior and singularity regularization, SciPost Phys., 10, 022 (2021) · doi:10.21468/scipostphys.10.1.022
[29] Sartini, F.; Geiller, M., Quantum dynamics of the black hole interior in loop quantum cosmology, Phys. Rev. D, 103 (2021) · doi:10.1103/physrevd.103.066014
[30] Nicolini, P.; Spallucci, E.; Wondrak, M. F., Quantum corrected black holes from string T-duality, Phys. Lett. B, 797 (2019) · doi:10.1016/j.physletb.2019.134888
[31] Easson, D. A.; Keeler, C.; Manton, T., The classical double copy of non-singular black holes (2020)
[32] Adéìféoba, A.; Eichhorn, A.; Platania, A. B., Towards conditions for black-hole singularity-resolution in asymptotically safe quantum gravity, Class. Quantum Grav., 35 (2018) · Zbl 1431.83046 · doi:10.1088/1361-6382/aae6ef
[33] Platania, A., Dynamical renormalization of black-hole spacetimes, Eur. Phys. J. C, 79, 470 (2019) · doi:10.1140/epjc/s10052-019-6990-2
[34] Moti, R.; Shojai, A., On the quantum improved Schwarzschild black hole, Int. J. Mod. Phys. A, 35, 2050016 (2020) · doi:10.1142/s0217751x20500165
[35] Nicolini, P., Noncommutative black holes, the final appeal to quantum gravity: a review, Int. J. Mod. Phys. A, 24, 1229-1308 (2009) · Zbl 1170.83417 · doi:10.1142/s0217751x09043353
[36] Nicolini, P.; Smailagic, A.; Spallucci, E., Remarks on regular black holes, Int. J. Geom. Methods Mod. Phys., 15, 1850018 (2018) · Zbl 1380.83057 · doi:10.1142/s0219887818500184
[37] Smailagic, A.; Spallucci, E., ‘Kerrr’ black hole: the lord of the string, Phys. Lett. B, 688, 82-87 (2010) · doi:10.1016/j.physletb.2010.03.075
[38] Bardeen, J. M., Non-singular general relativistic gravitational collapse (1968)
[39] Hayward, S. A., Formation and evaporation of nonsingular black holes, Phys. Rev. Lett., 96 (2006) · doi:10.1103/physrevlett.96.031103
[40] Dymnikova, I., Vacuum nonsingular black hole, Gen. Relativ. Gravit., 24, 235-242 (1992) · doi:10.1007/bf00760226
[41] Dymnikova, I. G., De Sitter-Schwarzschild black hole: its particlelike core and thermodynamical properties, Int. J. Mod. Phys. D, 05, 529-540 (1996) · doi:10.1142/s0218271896000333
[42] Frolov, V. P., Notes on nonsingular models of black holes, Phys. Rev. D, 94 (2016) · doi:10.1103/physrevd.94.104056
[43] Frolov, V. P., Remarks on non-singular black holes, EPJ Web Conf., 168, 01001 (2018) · doi:10.1051/epjconf/201816801001
[44] Ashtekar, A.; Bojowald, M., Black hole evaporation: a paradigm, Class. Quantum Grav., 22, 3349-3362 (2005) · Zbl 1160.83332 · doi:10.1088/0264-9381/22/16/014
[45] Haggard, H. M.; Rovelli, C., Quantum-gravity effects outside the horizon spark black to white hole tunneling, Phys. Rev. D, 92 (2015) · doi:10.1103/physrevd.92.104020
[46] Bianchi, E.; Christodoulou, M.; D’Ambrosio, F.; Haggard, H. M.; Rovelli, C., White holes as remnants: a surprising scenario for the end of a black hole, Class. Quantum Grav., 35 (2018) · doi:10.1088/1361-6382/aae550
[47] Martin-Dussaud, P.; Rovelli, C., Evaporating black-to-white hole, Class. Quantum Grav., 36 (2019) · Zbl 1478.83167 · doi:10.1088/1361-6382/ab5097
[48] Kiefer, C.; Schmitz, T., Singularity avoidance for collapsing quantum dust in the Lemaître-Tolman-Bondi model, Phys. Rev. D, 99 (2019) · doi:10.1103/physrevd.99.126010
[49] Schmitz, T., Towards a quantum Oppenheimer-Snyder model, Phys. Rev. D, 101 (2020) · doi:10.1103/physrevd.101.026016
[50] Piechocki, W.; Schmitz, T., Quantum Oppenheimer-Snyder model, Phys. Rev. D, 102 (2020) · doi:10.1103/physrevd.102.046004
[51] Modesto, L., Gravitational collapse in loop quantum gravity, Int. J. Theor. Phys., 47, 357-373 (2008) · Zbl 1140.83354 · doi:10.1007/s10773-007-9458-3
[52] Husain, V., Critical behaviour in quantum gravitational collapse (2008)
[53] Hossenfelder, S.; Modesto, L.; Prémont-Schwarz, I., Model for nonsingular black hole collapse and evaporation, Phys. Rev. D, 81 (2010) · doi:10.1103/physrevd.81.044036
[54] Bambi, C.; Malafarina, D.; Modesto, L., Non-singular quantum-inspired gravitational collapse, Phys. Rev. D, 88 (2013) · doi:10.1103/physrevd.88.044009
[55] Bojowald, M.; Goswami, R.; Maartens, R.; Singh, P., Black hole mass threshold from nonsingular quantum gravitational collapse, Phys. Rev. Lett., 95 (2005) · doi:10.1103/physrevlett.95.091302
[56] Barceló, C.; Carballo-Rubio, R.; Garay, L. J.; Jannes, G., The lifetime problem of evaporating black holes: mutiny or resignation, Class. Quantum Grav., 32 (2015) · Zbl 1312.83023 · doi:10.1088/0264-9381/32/3/035012
[57] Chakrabarty, H.; Abdujabbarov, A.; Malafarina, D.; Bambi, C., A toy model for a baby universe inside a black hole, Eur. Phys. J. C, 80, 373 (2020) · doi:10.1140/epjc/s10052-020-7964-0
[58] Casadio, R., Hamiltonian formalism for the Oppenheimer-Snyder model, Phys. Rev. D, 58 (1998) · doi:10.1103/physrevd.58.064013
[59] Baccetti, V.; Murk, S.; Terno, D. R., Black hole evaporation and semiclassical thin shell collapse, Phys. Rev. D, 100 (2019) · doi:10.1103/physrevd.100.064054
[60] Hossenfelder, S.; Smolin, L., Conservative solutions to the black hole information problem, Phys. Rev. D, 81 (2010) · doi:10.1103/physrevd.81.064009
[61] Manna, G., Gravitational collapse for the K-essence emergent Vaidya spacetime, Eur. Phys. J. C, 80, 813 (2020) · doi:10.1140/epjc/s10052-020-8383-y
[62] Bonanno, A.; Khosravi, A-P; Saueressig, F., Regular black holes have stable cores, Phys. Rev. Lett., 96 (2020) · doi:10.1103/physrevlett.96.031103
[63] Malafarina, D., Classical collapse to black holes and quantum bounces: a review, Universe, 3, 48 (2017) · doi:10.3390/universe3020048
[64] Adler, R. J.; Bjorken, J. D.; Chen, P.; Liu, J. S., Simple analytical models of gravitational collapse, Am. J. Phys., 73, 1148-1159 (2005) · doi:10.1119/1.2117187
[65] Chatterjee, A.; Ghosh, A.; Jaryal, S. C., Marginally trapped surfaces in spherical gravitational collapse, Phys. Rev. D, 102 (2020) · doi:10.1103/physrevd.102.064048
[66] Oppenheimer, J. R.; Snyder, H., On continued gravitational contraction, Phys. Rev., 56, 455-459 (1939) · Zbl 0022.28104 · doi:10.1103/physrev.56.455
[67] Datt, B., Über eine Klasse von Lösungen der Gravitationsgleichungen der Relativität, Z. Phys., 108, 314-321 (1938) · Zbl 0018.18606 · doi:10.1007/bf01374951
[68] Israel, W., Singular hypersurfaces and thin shells in general relativity, Nuov Cim. B, 44, 1-14 (1966) · doi:10.1007/bf02710419
[69] Darmois, G., Les équations de la gravitation einsteinienne (1927), Paris:: Gauthier-Villars, Paris: · JFM 53.0816.03
[70] Achour, J. B.; Brahma, S.; Uzan, J-P, Bouncing compact objects. Part I. Quantum extension of the Oppenheimer-Snyder collapse, J. Cosmol. Astropart. Phys. (2020) · Zbl 1490.85002 · doi:10.1088/1475-7516/2020/03/041
[71] Ben Achour, J.; Uzan, J-P, Bouncing compact objects. II. Effective theory of a pulsating Planck star, Phys. Rev. D, 102 (2020) · doi:10.1103/physrevd.102.124041
[72] Achour, J. B.; Brahma, S.; Mukohyama, S.; Uzan, J-P, Towards consistent black-to-white hole bounces from matter collapse (2020) · Zbl 1493.83019
[73] Bojowald, M.; Brahma, S.; Reyes, J. D., Covariance in models of loop quantum gravity: spherical symmetry, Phys. Rev. D, 92 (2015) · doi:10.1103/physrevd.92.045043
[74] Bojowald, M., No-go result for covariance in models of loop quantum gravity, Phys. Rev. D, 102 (2020) · doi:10.1103/physrevd.102.046006
[75] Bojowald, M., Black-hole models in loop quantum gravity (2020)
[76] Arruga, D.; Achour, J. B.; Noui, K., Deformed general relativity and quantum black holes interior (2019)
[77] Birkhoff, G. D., Relativity and Modern Physics (1927), Cambridge, MA: Harvard University Press, Cambridge, MA
[78] Jebsen, J. T., On the general spherically symmetric solutions of Einstein’s gravitational equations in vacuo, Gen. Relativ Gravit., 37, 2253-2259 (2005) · Zbl 1093.83002 · doi:10.1007/s10714-005-0168-y
[79] Fayos, F.; Jaen, X.; Llanta, E.; Senovilla, J. M M., Matching of the Vaidya and Robertson-Walker metric, Class. Quantum Grav., 8, 2057-2068 (1991) · doi:10.1088/0264-9381/8/11/015
[80] Fayos, F.; Jaén, X.; Llanta, E.; Senovilla, J. M M., Interiors of Vaidya’s radiating metric: gravitational collapse, Phys. Rev. D, 45, 2732-2738 (1992) · Zbl 1232.83049 · doi:10.1103/physrevd.45.2732
[81] Fayos, F.; Senovilla, J. M M.; Torres, R., General matching of two spherically symmetric spacetimes, Phys. Rev. D, 54, 4862-4872 (1996) · doi:10.1103/physrevd.54.4862
[82] Nzioki, A. M.; Goswami, R.; Dunsby, P. K S., Jebsen-Birkhoff theorem and its stability in f(R) gravity, Phys. Rev. D, 89 (2014) · doi:10.1103/physrevd.89.064050
[83] Li, X-z; Zhai, X-h; Li, P., Generalized Birkhoff theorem and its applications in mimetic gravity (2018)
[84] Cavaglia, M.; de Alfaro, V.; Filippov, A. T., The Birkhoff theorem in the quantum theory of two-dimensional dilaton gravity (1997) · Zbl 1037.81099
[85] Kehm, D.; Kirsch, J.; Struckmeier, J.; Vasak, D.; Hanauske, M., Violation of Birkhoff’s theorem for pure quadratic gravity action, Astron. Nachr., 338, 1015-1018 (2017) · doi:10.1002/asna.201713421
[86] Devecioglu, D. O.; Park, M-I, Birkhoff’s theorem in Horava gravity, Phys. Rev. D, 99 (2019) · doi:10.1103/physrevd.99.104068
[87] Szabados, L. B., Quasi-local energy-momentum and angular momentum in GR: a review article, Living Rev. Relativ., 7, 4 (2004) · Zbl 1068.83506 · doi:10.12942/lrr-2004-4
[88] Fließbach, T., Allgemeine Relativitätstheorie (2012), Heidelberg: Springer, Heidelberg · Zbl 1252.83001
[89] Wald, R. M., General Relativity (1984), Chicago, IL: University of Chicago Press, Chicago, IL · Zbl 0549.53001
[90] Misner, C. W.; Thorne, K. S.; Wheeler, J. A., Gravitation (1973), San Francisco, CA: Freeman, San Francisco, CA
[91] Blanchette, K.; Das, S.; Hergott, S.; Rastgoo, S., Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity, Phys. Rev. D, 103 (2021) · doi:10.1103/physrevd.103.084038
[92] Bouhmadi-López, M.; Brahma, S.; Chen, C-Y; Chen, P.; Yeom, D-h, A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes (2020) · Zbl 1492.83056
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