Black hole entropy from classical Liouville theory | Zendy

Alex Giacomini | Zendy; Nicola Pinamonti | Zendy

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Black hole entropy from classical Liouville theory

Author(s) -

Alex Giacomini,

Nicola Pinamonti

Publication year - 2003

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2003/02/014

Subject(s) - virasoro algebra , ansatz , mathematical physics , liouville field theory , physics , central charge , conformal map , black hole (networking) , conformal field theory , black hole thermodynamics , entropy (arrow of time) , witt algebra , conformal symmetry , circular symmetry , rotating black hole , mathematics , quantum mechanics , algebra representation , pure mathematics , lie algebra , algebra over a field , quantum , mathematical analysis , quantum gravity , lie conformal algebra , cellular algebra , routing (electronic design automation) , angular momentum , computer network , routing protocol , computer science , adjoint representation of a lie algebra , link state routing protocol , relationship between string theory and quantum field theory

In this article we compute the black hole entropy by finding a classicalcentral charge of the Virasoro algebra of a Liouville theory using the Cardyformula. This is done by performing a dimensional reduction of the EinsteinHilbert action with the ansatz of spherical symmetry and writing the metric inconformally flat form. We obtain two coupled field equations. Using the nearhorizon approximation the field equation for the conformal factor decouples.The one concerning the conformal factor is a Liouville equation, it posses thesymmetry induced by a Virasoro algebra. We argue that it describes themicrostates of the black hole, namely the generators of this symmetry do notchange the thermodynamical properties of the black hole.Comment: LaTeX, 11 pages, to appear on JHE

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