Black hole entropy from classical Liouville theory

Details Black hole entropy from classical Liouville theory Black hole entropy from classical Liouville theory

2003-01-10

arxiv.org/abs/gr-qc/0301038v2

JHEP 0302 (2003) 014

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 11 pages, to appear on JHEP

Scientific paper

10.1088/1126-6708/2003/02/014

In this article we compute the black hole entropy by finding a classical central charge of the Virasoro algebra of a Liouville theory using the Cardy formula. This is done by performing a dimensional reduction of the Einstein Hilbert action with the ansatz of spherical symmetry and writing the metric in conformally flat form. We obtain two coupled field equations. Using the near horizon approximation the field equation for the conformal factor decouples. The one concerning the conformal factor is a Liouville equation, it posses the symmetry induced by a Virasoro algebra. We argue that it describes the microstates of the black hole, namely the generators of this symmetry do not change the thermodynamical properties of the black hole.

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