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General logarithmic corrections to black-hole entropy. (English) Zbl 1003.83025

Summary: We compute leading-order corrections to the entropy of any thermodynamic system due to small statistical fluctuations around equilibrium. When applied to black holes, these corrections are shown to be of the form \(-k\ln(\text{Area})\). For BTZ black holes, \(k= 3/2\), as found earlier. We extend the result to anti-de Sitter Schwarzschild and Reissner-Nordström black holes in arbitrary dimensions. Finally we examine the role of conformal field theory in black-hole entropy and its corrections.

MSC:

83C57 Black holes
80A10 Classical and relativistic thermodynamics
83C50 Electromagnetic fields in general relativity and gravitational theory
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