×

zbMATH — the first resource for mathematics

Black hole entropy from loop quantum gravity. (English) Zbl 0955.83506
Summary: We study the idea that the statistical entropy governing thermal interactions of a black hole with its exterior is determined by the microstates of the hole having distinct effects on the exterior, and over which a hole in a given macroscopic configuration thermally fluctuates. We argue that for a (macroscopically) Schwarzschild black hole this ensemble is formed by horizons with the same area. We compute the number of states in this ensemble from first principles using nonperturbative loop quantum gravity. We obtain a statistical entropy proportional to the area, as in the Bekenstein-Hawking formula.

MSC:
83C57 Black holes
81T20 Quantum field theory on curved space or space-time backgrounds
83C45 Quantization of the gravitational field
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] J. D. Bekenstein, in: Quantum Field Theory on Curved Spacetime and Black Hole Thermodynamics (1994)
[2] G. Gibbons, Phys. Lett. B 375 pp 37– (1996) · doi:10.1016/0370-2693(95)01565-5
[3] C. Rovelli, in: Quantum Gravity and Cosmology, (1992)
[4] R. DePietri, Phys. Rev. D 54 pp 2664– (1996) · doi:10.1103/PhysRevD.54.2664
[5] J. W. York, Phys. Rev. D 28 pp 2929– (1983) · Zbl 1370.83033 · doi:10.1103/PhysRevD.28.2929
[6] D. Christodoulou, Phys. Rev. Lett. 25 pp 1596– (1970) · doi:10.1103/PhysRevLett.25.1596
[7] D. Christodoulou, Phys. Rev. D 4 pp 3552– (1971) · doi:10.1103/PhysRevD.4.3552
[8] L. Susskind, Phys. Rev. D 48 pp 3743– (1993) · doi:10.1103/PhysRevD.48.3743
[9] A. Buonanno, Nucl. Phys. B451 pp 677– (1995) · Zbl 0925.83034 · doi:10.1016/0550-3213(95)00351-R
[10] M. Maggiore, Nucl. Phys. B429 pp 205– (1994) · Zbl 1009.83509 · doi:10.1016/S0550-3213(94)80047-2
[11] K. Thorne, in: Black Holes: The Membrane Paradigm (1986)
[12] D. Carlip, Nucl. Phys. B461 pp 581– (1996)
[13] S. Hawking, Commun. Math. Phys. 25 pp 152– (1972) · doi:10.1007/BF01877517
[14] C. Isham, J. Math. Phys. (N.Y.) 36 (1995) · Zbl 0882.46031 · doi:10.1063/1.531267
[15] C. Rovelli, Phys. Rev. D 52 pp 5743– (1995) · doi:10.1103/PhysRevD.52.5743
[16] A. Ashtekar, Phys. Rev. Lett. 69 pp 237– (1992) · Zbl 0968.83510 · doi:10.1103/PhysRevLett.69.237
[17] C. Rovelli, Class. Quantum Gravity 10 pp 1549– (1993) · Zbl 0800.83002 · doi:10.1088/0264-9381/10/8/015
[18] A. Connes, Class. Quantum Gravity 11 pp 2899– (1994) · Zbl 0821.46086 · doi:10.1088/0264-9381/11/12/007
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.