Abstract
This survey intends to cover recent approaches to black hole entropy which attempt to go beyond the standard semiclassical perspective. Quantum corrections to the semiclassical Bekenstein-Hawking area law for black hole entropy, obtained within the quantum geometry framework, are treated in some detail. Their ramification for the holographic entropy bound for bounded stationary spacetimes is discussed. Four dimensional supersymmetric extremal black holes in string-based N=2 supergravity are also discussed, albeit more briefly.
Similar content being viewed by others
References
S Chandrasekhar, Truth and Beauty (Chicago, 1987) pp. 153–154
J Bekenstein, Phys. Rev. D7, 2333 (1973)
S Hawking, Comm. Math. Phys. 43, 190 (1975)
J Bardeen, B Carter and S Hawking, Comm. Math. Phys. 31, 161 (1973)
S Carlip, Class. Quantum Gravit. 16, 3327 (1999)
J Wheeler, It from bit edited by L Keldysh and V Feinberg, Sakharov Memorial Lecture on Physics (Nova, 1992) vol. 2
G ’t Hooft, Dimensional reduction in quantum gravity in Salam festschrift edited by A Alo, J Ellis and S Randjbar-Daemi (World Scientific, 1993) gr-qc/9310006
L Susskind, J. Math. Phys. 36, 6377 (1995)
J Bekenstein, Phys. Rev. D9, 3292 (1974)
For a comprehensive review: see L Smolin, The strong and weak holographic principles, hepth/0003056 and references therein
R Mann and S Solodukhin, Nucl. Phys. B523, 293 (1998) and references therein
R Arnowitt, S Deser and C Misner in Gravitation: An Introduction to Current Research edited by L Witten (Wiley, 1967)
A Ashtekar, Lectures on non-pertubative quantum gravity (World Scientific, 1991)
Amitabha Sen, Phys. Lett. B119, 89 (1982)
F Barbero, Phys. Rev. B51, 5507 (1995)
G Immirzi, Nucl. Phys. Proc. Suppl. 57, 65 (1997)
Here Θ BC P is the standard Levi-Civita connection, i, j = 1, 2, 3 are spatial world indices, and a, b, c = 1, 2, 3 are spatial trangent space indices, and gij is the 3-metric
C Rovelli, Loop Quantum Gravity, gr-qc/9710008
C Rovelli and L Smolin, Phys. Rev. D52, 5743 (1995)
S Fritelli, L Lehner and C Rovelli, Class. Quantum Gravit. 13, 2921 (1996)
A Ashtekar and J Lewandowski, Class. Quantum Gravit. 14, 55 (1997) and references therein
K Krasnov, on quantum statistical mechanics of a Schwarzschild black hole, gr-qc/9605047; Quantum geometry and thermal radiation from black holes, gr-qc/9710006
A Ashtekar, J Baez, A Corichi and K Krasnov, Phys. Rev. Lett. 80, 904 (1998)
A Ashtekar, J Baez and K Krasnov, Quantum geometry of isolated horizons and black hole entropy, gr-qc/0005126
R Kaul and P Majumdar, Phys. Lett. B439, 267 (1998)
P Majumdar, Indian J. Phys. B43, 147 (1998)
R Kaul, Topological field theories — a meeting ground for physicists and mathematicians, in Quantum Field Theory: A 20th Century Profile edited by A N Mitra (Hindustan Book Agency, India and Indian National Science Academy, New Delhi, 2000) p. 211
A Ashtekar, C Beetle and S Fairhurst, Mechanics of isolated horizons, gr-qc/9907068 and references therein
The latter symmetry, in particular, as already mentioned, implies that the location of punctures on S cannot have any physical significance
E Witten, Comm. Math. Phys. 121, 351 (1989)
P Di Francesco, P Mathieu and D Senechal, Conformal field theory, et seq (Springer Verlag, 1997) p. 375
R Kaul and P Majumdar, Phys. Rev. Lett. 84, 5255 (2000)
S Carlip, Logarithmic corrections to black hole entropy from Cardy formula, gr-qc/0005017
Spacetimes like the interior geometry of a black hole or expanding cosmological spacetimes lie outside the purview of this analysis, since even the Bekenstein bound is not valid for them [33,34].
S Ferrara, R Kallosh and A Strominger, Phys. Rev. D52, 5412 (1995)
A Strominger, Phys. Lett. B383, 39 (1996)
S D Majumdar, Phys. Rev. 72, 390 (1947)
A Papapetrou, Proc. R. Ir. Ac. A51, 191 (1947)
J Maldacena, A Strominger and E Witten, J. High Energy Phys. 12, 2 (1997)
W Fischler and L Susskind, Holography and Cosmology, hep-th/9806039
R Bousso, Class. Quantum Gravit. 17, 997 (2000) and references therein
B de Wit, Modifications of the area law and N = 2 supersymmetric black holes, hepth/9906095 and references therein
R Wald, Phys. Rev. D48, 3427 (1993)
V Iyer and R Wald, Phys. Rev. D50, 846 (1994)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Majumdar, P. Quantum aspects of black hole entropy. Pramana - J Phys 55, 511–527 (2000). https://doi.org/10.1007/s12043-000-0163-5
Issue Date:
DOI: https://doi.org/10.1007/s12043-000-0163-5