A Century of Black Hole Physics: From Classical Geometry to Hawking Radiation and the Firewall Controversy

  • Yen Chin OngEmail author
Part of the Springer Theses book series (Springer Theses)


This introductory chapter aims to provide a history of the field, from the early days when Einstein first formulated his general theory of relativity, and discoveries of black hole solutions in the theory, to the later debates about the as yet unresolved information loss paradox and the firewall controversy today. Most of this chapter is written in the style of a semipopular science article. The aim is to convey, at least partially, the results of this thesis to a wider audience, who are not necessarily trained in physics beyond that of their high school education. The use of equations will be kept to a minimum (some equations are included since they represent major milestones in the history of black hole physics; these will be further elaborated on in Chap.  2). Some technical statements are provided in footnotes and boxes.


Black Hole Event Horizon Black Hole Solution Black Hole Physic Large Black Hole 
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  1. 1.
    Einstein, A.: Feldgleichungen der gravitation, Sitzungsberichte, Preussische Akademie der Wissenschaften, p. 844 (1915)Google Scholar
  2. 2.
    Einstein, A.: Erklärung der perihelbewegung des Merkur aus der allgemeinen relativitätstheorie, Sitzungsberichte, Preussische Akademie der Wissenschaften, p. 831 (1915)Google Scholar
  3. 3.
    Chandrasekhar, S.: The general theory of relativity: why it is probably the most beautiful of all existing theories. J. Astrophys. Astron. 5, 3 (1984)ADSCrossRefGoogle Scholar
  4. 4.
    Ferreira, P.G.: The perfect theory: a century of geniuses and the battle over general relativity. Mariner Books (2014)Google Scholar
  5. 5.
    Ford, K.W., Wheeler, J.A.: Geons, black holes, and quantum foam: a life in physics, 1st edn, p. 235. W. W. Norton & Company (2000)Google Scholar
  6. 6.
    Schwarzschild, K.: On the gravitational field of a mass point according to Einstein’s theory. Sitzungsber. Preuss. Akad. Wiss. Berlin (Math.Phys.) 189 (1916). arXiv:physics/9905030 [physics.hist-ph]
  7. 7.
    Siegfried, T.: 50 years later, it’s hard to say who named black holes. Science News.’s-hard-say-who-named-black-holes. Accessed 16 April 2014
  8. 8.
    Droste, J.: The field of a single centre in Einstein’s theory of gravitation, and the motion of a particle in that field, reprinted in Gen. Rel. Gravity 34, 1545 (2002)Google Scholar
  9. 9.
    Oppenheimer, J.R., Snyder, H.: On continued gravitational contraction. Phys. Rev. 56, 455 (1939)Google Scholar
  10. 10.
    Christodoulou, D.: The formation of black holes in general relativity. European Mathematical Society Publishing House, Zurih (2009). arXiv:0805.3880 [gr-qc]
  11. 11.
    Eddington, A.: Space, time and gravitation. Cambridge University Press (1920)Google Scholar
  12. 12.
    Hilbert, D.: Die grundlagen der physik II, Vorlesung, Wintersemester 1916–17, ausgearbeitet von R. Bär, Mathematisches Institut, Universität GöttingenGoogle Scholar
  13. 13.
    Kruskal, M.: Maximal extension of Schwarzschild metric. Phys. Rev. 119, 1743 (1960)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Zee, A.: Einstein’s gravity in a nutshell. Princeton University Press (2013)Google Scholar
  15. 15.
    Wheeler, J.A.: The lesson of the black hole. Proc. Am. Philos. Soc. 125, 25 (1981)Google Scholar
  16. 16.
    Reissner, H.: Über die eigengravitation des elektrischen feldes nach der Einsteinschen theorie. Annalen der Physik 50, 106 (1916)Google Scholar
  17. 17.
    Nordström, G.: On the energy of the gravitational field in Einstein’s theory. Verhandl. Koninkl. Ned. Akad. Wetenschap. Afdel. Natuurk. Amsterdam 26, 1201 (1918)Google Scholar
  18. 18.
    Kerr, R.: Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11, 237 (1963)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Kerr, R.: Discovering the Kerr and Kerr-Schild metrics. arXiv:0706.1109 [gr-qc]
  20. 20.
    Boyer, R.H., Lindquist, R.W.: Maximal analytic extension of the Kerr metric. J. Math. Phys. 8, 265 (1967)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Visser, M.: The Kerr spacetime: a brief introduction. arXiv:0706.0622 [gr-qc]
  22. 22.
    Newman, E., Janis, A.: Note on the Kerr spinning-particle metric. J. Math. Phys. 6, 915 (1965)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Newman, E., Couch, E., Chinnapared, K., Exton, A., Prakash, A., Torrence, R.: Metric of a rotating, charged mass. J. Math. Phys. 6(6), 918 (1965)Google Scholar
  24. 24.
    Chandrasekhar, S.: Shakespeare, Newton, and Beethoven or patterns of creativity. Ryerson Lecture, University of Chicago (1975). Reprinted in S. Chandrasekhar, “Truth and Beauty”, University of Chicago Press (1987)Google Scholar
  25. 25.
    Painlevé, P.: La mécanique classique et la théorie de la relativité. C. R. Acad. Sci. (Paris) 173, 677 (1921)Google Scholar
  26. 26.
    Gullstrand, A.: Allgemeine lösung des statischen einkörperproblems in der Einsteinschen gravitationstheorie. Arkiv. Mat. Astron. Fys. 16(8), 1 (1922)Google Scholar
  27. 27.
    Birkhoff, G.D.: Relativity and modern physics. Harvard University Press, Cambridge (1923)Google Scholar
  28. 28.
    Jebsen, J.T.: On the general spherically symmetric solutions of Einstein’s gravitational equations in vacuo. Arkiv. Mat. Astron. Fys. 15, 18 (1921)Google Scholar
  29. 29.
    Israel, W.: Event horizons in static vacuum space-times. Phys. Rev. 164, 1776 (1967)ADSCrossRefGoogle Scholar
  30. 30.
    Ruffini, R., Wheeler, J.A.: Introducing the black hole. Phys. Today 24, 30 (1971)Google Scholar
  31. 31.
    Mazur, P.O.: Proof of uniqueness of the Kerr-Newman black hole solution. J. Phys. A: Math. Gen. 15, 3173 (1982)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  32. 32.
    Heusler, M.: Black hole uniqueness theorems. Number 6 in Cambridge lecture notes in physics. Cambridge University Press (1996)Google Scholar
  33. 33.
    Price, R.H.: Nonspherical perturbations of relativistic gravitational collapse. Phys. Rev. D 5, 2419 (1972)ADSCrossRefMathSciNetGoogle Scholar
  34. 34.
    Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. Cambridge University Press (1973)Google Scholar
  35. 35.
    Carter, B.: An axy-symmetric black hole has only two degrees of freedom. Phys. Rev. Lett. 26, 331 (1971)ADSCrossRefGoogle Scholar
  36. 36.
    Robinson, D.C.: Uniqueness of the Kerr black hole. Phys. Rev. Lett. 34, 905 (1975)ADSCrossRefGoogle Scholar
  37. 37.
    Ionescu, A.D., Klainerman, S.: On the uniqueness of smooth, stationary black holes in vacuum. Inventiones Mathematicae 175, 35 (2009)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  38. 38.
    Alexakis, S., Ionescu, A.D., Klainerman, S.: Uniqueness of smooth stationary black holes in vacuum: small perturbations of the Kerr spaces. Commun. Math. Phys. 299, 89 (2010). arXiv:0904.0982 [gr-qc]Google Scholar
  39. 39.
    Mavromatos, N.E.: Eluding the no-hair conjecture for black holes. arXiv:gr-qc/9606008
  40. 40.
    Hod, S.: Rotating black holes can have short bristles. Phys. Lett. B 739, 196 (2014). arXiv:1411.2609 [gr-qc]Google Scholar
  41. 41.
    Herdeiro, C.A.R., Radu, E.: Asymptotically flat black holes with scalar hair: a review. Int. J. Mod. Phys. D 24, 1542014 (2015). arXiv:1504.08209 [gr-qc]Google Scholar
  42. 42.
    Sotiriou, T.P.: Black holes and scalar fields. Class. Quant. Grav. 32, 214002 (2015). arXiv:1505.00248 [gr-qc]Google Scholar
  43. 43.
    Gürlebeck, N.: No-hair theorem for black holes in astrophysical environments. Phys. Rev. Lett. 114, 15, 151102 (2015). arXiv:1503.03240 [gr-qc]
  44. 44.
    Ashtekar, A.: Viewpoint: Simplicity of black holes. Physics 8, 24 (2015). arXiv:1504.07693 [gr-qc]
  45. 45.
    Spolyar, D., Freese, K., Gondolo, P.: Dark matter and the first stars: a new phase of stellar evolution. Phys. Rev. Lett. 100, 051101 (2008). arXiv:0705.0521 [astro-ph]
  46. 46.
    Freese, K., Rindler-Daller, T., Spolyar, D., Valluri, M.: Dark stars: a review. arXiv:1501.02394 [astro-ph.CO]
  47. 47.
    Curiel, E.: A primer on energy conditions. arXiv:1405.0403 [physics.hist-ph]
  48. 48.
    Hawking, S.W.: Black holes in general relativity. Commun. Math. Phys. 25, 87 (1972)ADSCrossRefMathSciNetGoogle Scholar
  49. 49.
    Bardeen, J.M., Carter, B., Hawking, S.W.: The four laws of black hole mechanics. Comm. Math. Phys. 31, 161 (1973)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  50. 50.
    Bekenstein, J.: Black holes and entropy. Phys. Rev. D 7, 2333 (1973)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  51. 51.
    Page, D.N.: Hawking radiation and black hole thermodynamics. New J. Phys. 7, 203 (2005). arXiv:hep-th/0409024Google Scholar
  52. 52.
    Hawking, S.W.: Black hole explosions? Nature 248, 30 (1974)ADSCrossRefzbMATHGoogle Scholar
  53. 53.
    Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  54. 54.
    Chen, P., Wang, C.-H.: Where is hbar hiding in entropic gravity? arXiv:1112.3078 [gr-qc]
  55. 55.
    Curiel, E.: Classical black holes are hot. arXiv:1408.3691 [gr-qc]
  56. 56.
    Fulling, S.A.: Nonuniqueness of canonical field quantization in Riemannian space-time. Phys. Rev. D 7, 2850 (1973)ADSCrossRefGoogle Scholar
  57. 57.
    Davies, P.C.W.: Scalar production in Schwarzschild and Rindler metrics. J. Phys. A 8, 609 (1975)ADSCrossRefGoogle Scholar
  58. 58.
    Unruh, W.G.: Notes on black-hole evaporation. Phys. Rev. D 14, 870 (1976)ADSCrossRefGoogle Scholar
  59. 59.
    Rosu, H.C.: Noninertial quantum mechanical fluctuations. Artificial black holes, pp. 307–334. World Scientific (2002). arXiv:gr-qc/0012083
  60. 60.
    Letaw, J.R.: Stationary world lines and the vacuum excitation of noninertial detectors. Phys. Rev. D 23, 1709 (1981)ADSCrossRefMathSciNetGoogle Scholar
  61. 61.
    Brynjolfsson, E.J., Thorlacius, L.: Taking the temperature of a black hole. JHEP 0809, 066 (2008). arXiv:0805.1876 [hep-th]Google Scholar
  62. 62.
    Visser, M.: Essential and inessential features of Hawking radiation. Int. J. Mod. Phys. D 12, 649 (2003). arXiv:hep-th/0106111Google Scholar
  63. 63.
    Brout, R., Massar, S., Parentani, R., Spindel, P.: Hawking radiation without transplanckian frequencies. Phys. Rev. D 52, 4559 (1995). arXiv:hep-th/9506121Google Scholar
  64. 64.
    Lambert, P.-H.: Introduction to black hole evaporation. PoS Modave 2013, 001 (2013). arXiv:1310.8312 [gr-qc]
  65. 65.
    Hawking, S.W.: Breakdown of predictability in gravitational collapse. Phys. Rev. D 14, 2460 (1976)ADSCrossRefMathSciNetGoogle Scholar
  66. 66.
    Penrose, R.: Singularities and time-asymmetry. In: Hawking, S.W., Israel, W. (eds.) General relativity: an Einstein centenary survey. Cambridge University Press (1979)Google Scholar
  67. 67.
    Price, H.: Cosmology, time’s arrow, and that old double standard. In: Savitt, S. (ed.) Time’s arrows today. Cambridge University Press (1994). arXiv:gr-qc/9310022, The thermodynamic arrow: puzzles and pseudo-puzzles. arXiv:physics:0402040, Time’s arrow and Eddington’s challenge, Séminaire Poincaré XV Le Temps, 115 (2010)
  68. 68.
    McInnes, B.: Arrow of time in string theory. Nucl. Phys. B 782, 1 (2007). arXiv:hep-th/0611088Google Scholar
  69. 69.
    McInnes, B.: The arrow of time in the landscape. arXiv:0711.1656 [hep-th]
  70. 70.
    Carroll, S.M., Chen, J.: Spontaneous inflation and the origin of the arrow of time. arXiv:hep-th/0410270
  71. 71.
    Carroll, S.: From eternity to here, Plume, Reprint Edition (2010)Google Scholar
  72. 72.
    von Neumann, J.: Mathematische grundlagen der quantenmechanik. Springer, Berlin (1955)zbMATHGoogle Scholar
  73. 73.
    Rényi, A.: On measures of information and entropy. In: Proceedings of the fourth Berkeley Symposium on Mathematics, Statistics and Probability, vol. 1960, p. 547 (1961)Google Scholar
  74. 74.
    Shannon, C.E.: A mathematical theory of communication. Syst. Tech. J. 27(3), 379 (1948)CrossRefzbMATHMathSciNetGoogle Scholar
  75. 75.
    Preskill, J.: Do black holes destroy information? In: Proceedings of Black holes, Membranes, Wormholes and Superstrings (1992). arXiv:hep-th/9209058
  76. 76.
    Wald, R.M.: The thermodynamics of black holes. Living Rev. Relat. 4, 6 (2001). Accessed 8 March 2014
  77. 77.
    Sekino, Y., Susskind, L.: Fast scramblers. JHEP 0810, 065 (2008). arXiv:0808.2096 [hep-th]Google Scholar
  78. 78.
    Susskind, L., Thorlacius, L., Uglum, J.: The stretched horizon and black hole complementarity. Phys. Rev. D 48, 3743 (1993). arXiv:hep-th/9306069Google Scholar
  79. 79.
    Susskind, L., Thorlacius, L.: Gedanken experiments involving black holes. Phys. Rev. D 49, 966 (1994). arXiv:hep-th/9308100Google Scholar
  80. 80.
    Almheiri, A., Marolf, D., Polchinski, J., Sully, J.: Black holes: complementarity or firewalls? JHEP 1302, 062 (2013). arXiv:1207.3123 [hep-th]
  81. 81.
    Bousso, R.: Observer complementarity upholds the equivalence principle. arXiv:1207.5192v1 [hep-th]
  82. 82.
    Bousso, R.: Complementarity is not enough. Phys. Rev. D 87, 124023 (2012). arXiv:1207.5192v2 [hep-th]
  83. 83.
    Myers, R.C.: Pure states don’t wear black. Gen. Rel. Gravity 29, 1217 (1997). arXiv:gr-qc/9705065Google Scholar
  84. 84.
    Page, D.N.: Average entropy of a subsystem. Phys. Rev. Lett. 71, 1291 (1993). arXiv:gr-qc/9305007Google Scholar
  85. 85.
    Page, D.N.: Information in black hole radiation. Phys. Rev. Lett. 71, 3743 (1993). arXiv:hep-th/9306083Google Scholar
  86. 86.
    Page, D.N.: Time dependence of Hawking radiation entropy. JCAP 1309, 028 (2013). arXiv:1301.4995 [hep-th]Google Scholar
  87. 87.
    Merali, Z.: Astrophysics: fire in the hole! Nature 496, 20 (2013). Accessed 21 April 2014Google Scholar
  88. 88.
    Hawking, S.W.: The chronology protection conjecture. Phys. Rev. D 46, 603 (1992)ADSCrossRefMathSciNetGoogle Scholar
  89. 89.
    Leonard, S.: The transfer of entanglement: the case for firewalls. arXiv:1210.2098 [hep-th]
  90. 90.
    Daniel, H., Patrick, H.: Quantum computation vs. firewalls. JHEP 06 085 (2013). arXiv:1301.4504 [hep-th]
  91. 91.
    Aaronson, S.: Firewalls. In :Shtetl-Optimized blog. Accessed 21 June 2015
  92. 92.
    Almheiri, A., Marolf, D., Polchinski, J., Stanford, D., Sully, J.: An apologia for firewalls. JHEP 1309, 018 (2013). arXiv:1304.6483 [hep-th]
  93. 93.
    Braunstein, S.L., Pirandola, S.: Post-firewall paradoxes. arXiv:1411.7195 [quant-ph]
  94. 94.
    Klebanov, I.R., Maldacena, J.M.: Solving quantum field theories via curved spacetimes. Phys. Today 62, 28 (2009)CrossRefGoogle Scholar
  95. 95.
    Mathur, S.D.: The information paradox: a pedagogical introduction. Class. Quant. Gravity 26, 224001 (2009). arXiv:0909.1038 [hep-th]Google Scholar
  96. 96.
    Hawking, S.W.: Information loss in black holes. Phys. Rev. D 72, 084013 (2005). arXiv:hep-th/0507171
  97. 97.
    Sakharov, A.D.: Vacuum quantum fluctuations in curved space and the theory of gravitation. Dokl. Akad. Nauk Ser. Fiz. 177, 70 (1967) (Gen. Rel. Grav. 32, 365 (2000))Google Scholar
  98. 98.
    Hiscock, W.A., Weems, L.D.: Evolution of charged evaporating black holes. Phys. Rev. D 41, 1142 (1990)ADSCrossRefGoogle Scholar
  99. 99.
    Wheeler, J.A.: Relativity, groups, and fields, edited by B.S. DeWitt and C.M. DeWitt. Gordon and Breach, New York (1964)Google Scholar
  100. 100.
    Smolin, L.: The fate of black hole singularities and the parameters of the standard models of particle physics and cosmology. arXiv:gr-qc/9404011
  101. 101.
    Smolin, L.: The status of cosmological natural selection. arXiv:hep-th/0612185
  102. 102.
    Dyson, F.: Institute for advanced study Preprint (1976) (unpublished)Google Scholar
  103. 103.
    Preskill, J.: Do black holes destroy information? arXiv:hep-th/9209058
  104. 104.
    Hossenfelder, S., Smolin, L.: Conservative solutions to the black hole information problem. Phys. Rev. D 81, 064009 (2010). arXiv:0901.3156 [gr-qc]
  105. 105.
    Chen, P., Ong, Y.C., Yeom, D.-h.: Black hole remnants and the information loss paradox. arXiv:1412.8366 [gr-qc]
  106. 106.
    Smolin, L.: The strong and weak holographic principles. Nucl. Phys. B 601, 209 (2001). arXiv:hep-th/0003056Google Scholar
  107. 107.
    Jacobson, T., Marolf, D., Rovelli, C.: Black hole entropy: inside or out? Int. J. Theor. Phys. 44, 1807 (2005). arXiv:hep-th/0501103Google Scholar
  108. 108.
    Marolf, D.: Black holes, AdS, and CFTs. Gen. Relat. Gravity 41, 903 (2009). arXiv:0810.4886 [gr-qc]Google Scholar
  109. 109.
    Hsu, S.D.H., Reeb, D.: Black hole entropy, curved space and monsters. Phys. Lett. B 658 244 (2008). arXiv:0706.3239 [hep-th]Google Scholar
  110. 110.
    Hsu, S.D.H., Reeb, D.: Monsters, black holes and the statistical mechanics of gravity. Mod. Phys. Lett. A 24, 1875 (2009). arXiv:0908.1265 [gr-qc]Google Scholar
  111. 111.
    Seiberg, N., Witten, E.: The D1/D5 system and singular CFT. JHEP 9904, 017 (1999). arXiv:hep-th/9903224Google Scholar
  112. 112.
    Kleban, M., Porrati, M., Rabadan, R.: Stability in asymptotically AdS spaces. JHEP 0508, 016 (2005). arXiv:hep-th/0409242Google Scholar
  113. 113.
    Barbón, J.L.F., Martínez-Magán, J.: Spontaneous fragmentation of topological black holes. JHEP 08 031 (2010). arXiv:1005.4439 [hep-th]
  114. 114.
    Hawking, S.W.: Information preservation and weather forecasting for black holes. arXiv:1401.5761 [hep-th]
  115. 115.
    Visser, M.: Black holes in general relativity. PoS BHs, GR and Strings 2008, 001 (2008). arXiv:0901.4365 [gr-qc]
  116. 116.
    Van Raamsdonk, M.: Comments on quantum gravity and entanglement. arXiv:0907.2939 [hep-th]
  117. 117.
    Van Raamsdonk, M.: Building up spacetime with quantum entanglement. Gen. Relat. Gravity 42, 2323 (2010) (Int. J. Mod. Phys. D 19, 2429 (2010)). arXiv:1005.3035 [hep-th]
  118. 118.
    Czech, B., Karczmarek, J.L., Nogueira, F., Van Raamsdonk, M.: Rindler quantum gravity. Class. Quant. Gravity 29, 235025 (2012). arXiv:1206.1323 [hep-th]Google Scholar
  119. 119.
    Horowitz, G.T., Maldacena, J.: The black hole final state. JHEP 0402, 008 (2004). arXiv:hep-th/0310281Google Scholar
  120. 120.
    Lloyd, S.: Almost certain escape from black holes in final state projection models. Phys. Rev. Lett. 96, 061302 (2006)ADSCrossRefMathSciNetGoogle Scholar
  121. 121.
    McInnes, B.: Black hole final state conspiracies. Nucl. Phys. B 807, 33 (2009). arXiv:0806.3818 [hep-th]Google Scholar
  122. 122.
    Mathur, S.D.: Fuzzballs and black hole thermodynamics. arXiv:1401.4097 [hep-th]
  123. 123.
    Einstein, A., Rosen, N.: The particle problem in the general theory of relativity. Phys. Rev. 48, 73 (1935)ADSCrossRefzbMATHGoogle Scholar
  124. 124.
    Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)Google Scholar
  125. 125.
    Maldacena, J., Susskind, L.: Cool horizons for entangled black holes. Fortsch. Phys. 61, 781 (2013). arXiv:1306.0533 [hep-th]Google Scholar
  126. 126.
    Baez, J.C., Vicary, J.: Wormholes and entanglement. arXiv:1401.3416 [gr-qc]
  127. 127.
    Bousso, R.: Firewalls from double purity. Phys. Rev. D 88, 084035 (2013). arXiv:1308.2665 [hep-th]
  128. 128.
    Bousso, R.: Violations of the equivalence principle by a nonlocally reconstructed vacuum at the black hole horizon. Phys. Rev. Lett. 112, 041102 (2014). arXiv:1308.3697 [hep-th]
  129. 129.
    Hutchinson, J., Stojkovic, D.: Icezones instead of firewalls: extended entanglement beyond the event horizon and unitary evaporation of a black hole. arXiv:1307.5861 [hep-th]
  130. 130.
    Rovelli, C., Vidotto, F.: Planck stars. Int. J. Mod. Phys. D 23, 1442026 (2014). arXiv:1401.6562 [gr-qc]Google Scholar
  131. 131.
    Barrau, A., Rovelli, C.: Planck star phenomenology. Phys. Lett. B 739, 405 (2014). arXiv:1404.5821 [gr-qc]Google Scholar
  132. 132.
    Barrau, A., Bolliet, B., Vidotto, F., Weimer, C.: Phenomenology of bouncing black holes in quantum gravity: a closer look. arXiv:1507.05424 [gr-qc]

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Authors and Affiliations

  1. 1.Nordic Institute for Theoretical PhysicsStockholmSweden

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