Black holes: Interfacing the classical and the quantum. (English) Zbl 1163.83347

Summary: The central idea of this paper is that forming the black hole horizon is attended with the transition from the classical regime of evolution to the quantum one. We offer and justify the following criterion for discriminating between the classical and the quantum: creations and annihilations of particle-antiparticle pairs are impossible in the classical reality but possible in the quantum reality. In flat spacetime, we can switch from the classical picture of field propagation to the quantum picture by changing the overall sign of the spacetime signature. To describe a self-gravitating object at the final stage of its classical evolution, we propose to use the Foldy-Wouthuysen representation of the Dirac equation in curved spacetimes, and the Gozzi classical path integral. In both approaches, maintaining the dynamics in the classical regime is controlled by supersymmetry.


83C57 Black holes
83C47 Methods of quantum field theory in general relativity and gravitational theory
81S40 Path integrals in quantum mechanics
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[1] Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. Freeman, San Francisco (1973)
[2] Chandrasekhar, S.: The Mathematical Theory of Black Holes. Oxford University Press, New York (1992) · Zbl 0912.53053
[3] Heusler, M.: Black Hole Uniqueness theorems. Cambridge University Press, Cambridge (1996) · Zbl 0945.83001
[4] Chruściel, P.T.: Black Holes. Lecture Notes in Physics, vol. 604, p. 61. Springer, Berlin (2002). arxivurl: gr-qc/0201053 · Zbl 1052.83023
[5] Carlip, S.: Black hole entropy from conformal field theory in any dimensions. Phys. Rev. Lett. 64, 435 (1976). arxivurl: hep-th/9812013
[6] Solodukhin, S.: Conformal description of horizon’s states. Phys. Lett. B 454, 213 (1999). arxivurl: hep-th/9812056 · Zbl 1009.83514
[7] Wilson, K.G.: Problems in physics with many scales of length. Sci. Am. 241, 158 (1979)
[8] Wilson, K.G.: The renormalization group and critical phenomena. Rev. Mod. Phys. 55, 583 (1983)
[9] Chapline, G., Hohfeld, E., Laughlin, R.B., Santiago, D.I.: Quantum phase transitions and breakdown of classical general relativity. Int. J. Mod. Phys. 18, 3587 (2003). arxivurl: gr-qc/0012094
[10] Laughlin, R.B.: Emergent relativity. Int. J. Mod. Phys. 18, 831 (2003). arxivurl: gr-qc/0302028 · Zbl 1044.83008
[11] Hawking, S.: Black hole explosions? Nature 248, 30 (1974) · Zbl 1370.83053
[12] Hawking, S.: Quantum particle creation by black hole. Commun. Math. Phys. 43, 199 (1975) · Zbl 1378.83040
[13] Hawking, S., Ellis, G.: The Large Structure of Space-Time. Cambridge University Press, Cambridge (1973) · Zbl 0265.53054
[14] Horowitz, G.T., Maldacena, J.: The black hole final state. J. High Energy Phys. 02, 008 (2004)
[15] Brink, L., Deser, S., Zumino, B., Di Vecchia, P., Howe, P.: Local supersymmetry for spinning particles. Phys. Lett. B 64, 435 (1976)
[16] Feynman, R.: The development of the space-time view of quantum electrodynamics. Phys. Today 19, 31 (1966)
[17] Kosyakov, B.: Introduction to the Classical Theory of Particles and Fields. Springer, Berlin (2007) · Zbl 1114.81003
[18] Foldy, L.L., Wouthuysen, S.A.: On the Dirac theory of spin- \(\frac{1}{2}\) particles and its nonrelativistic limit. Phys. Rev. 78, 29 (1950) · Zbl 0039.22605
[19] Case, K.M.: Some generalizations of the Foldy–Wouthuysen transformation. Phys. Rev. 95, 1323 (1954) · Zbl 0057.20601
[20] de Vries, E.: Foldy–Wouthuysen transformations and related problems. Fortschr. Phys. 18, 149 (1970)
[21] Thaller, B.: The Dirac Equation. Berlin, Springer (1992) · Zbl 0765.47023
[22] Obukhov, Yu.N.: Spin, gravity, and inertia. Phys. Rev. Lett. 86, 192 (2001). arxivurl: gr-qc/0012102
[23] Romero, R.P.M., Moreno, M., Zentella, A.: Supersymmetric properties and stability of the Dirac sea. Phys. Rev. D 43, 2036 (1991)
[24] Heidenreich, S., Chrobok, T., Borzeszkowski, H.-H. v.: Supersymmetry, exact Foldy–Wouthuysen transformation, and gravity. Phys. Rev. D 73, 044026 (2006)
[25] Galvao, C.A.P., Teitelboim, C.: Classical supersymmetric particles. J. Math. Phys. 21, 1863 (1980) · Zbl 0425.53016
[26] Gozzi, E.: Hidden BRS invariance in classical mechanics. Phys. Lett. 201, 525 (1988)
[27] Gozzi, E., Reuter, M., Thacker, W.D.: Hidden BRS invariance in classical mechanics, II. Phys. Rev. D 40, 3363 (1989)
[28] Abrikosov, A.A. Jr., Gozzi, E., Mauro, D.: Geometric dequantization. Ann. Phys. (N.Y.) 317, 24 (2005). arxivurl: quant-ph/0406028 · Zbl 1098.81050
[29] Jackiw, R., Nair, V.P., Pi, S.-Y., Polychronakos, A.P.: Perfect fluid theory and its extension. J. Phys. A 37, R327 (2004). arxivurl: hep-ph/0407101 · Zbl 1072.76004
[30] Robinson, S., Wilczek, F.: Relation between Hawking radiation and gravitational anomalies. Phys. Rev. Lett. 95, 011303 (2005). arxivurl: gr-qc/0502074v3
[31] Gozzi, E., Mauro, D., Silvestri, A.: Chiral anomalies via classical and quantum functional methods. Int. J. Mod. Phys. A 20, 5009 (2005). arxivurl: hep-th/0410129 · Zbl 1084.81052
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