A CFT description of the BTZ black hole: topology versus geometry (or thermodynamics versus statistical mechanics

TL;DR

This paper explores the entropy of BTZ black holes in AdS3 using conformal field theory, revealing topological and algebraic structures that relate to black hole dualities and modular symmetries.

Contribution

It establishes a CFT framework with a specific central charge to describe BTZ black hole horizons and links topological properties to conformal algebra extensions and dualities.

Findings

BTZ black hole entropy can be described by a 2D CFT with central charge c=1

The Virasoro algebra and SL(2,Z) modular symmetry relate to black hole dualities

A reanalysis of the Cardy formula in the context of black hole entropy

Abstract

In this paper we review the properties of the black hole entropy in the light of a general conformal field theory treatment. We find that the properties of horizons of the BTZ black holes in ADS_{3}, can be described in terms of an effective unitary CFT_{2} with central charge c=1 realized in terms of the Fubini-Veneziano vertex operators. It is found a relationship between the topological properties of the black hole solution and the infinite algebra extension of the conformal group in 2D, SU(2,2), i.e. the Virasoro Algebra, and its subgroup SL(2,Z) which generates the modular symmetry. Such a symmetry induces a duality for the black hole solution with angular momentum J\neq 0. On the light of such a global symmetry we reanalyze the Cardy formula for CFT_{2} and its possible generalization to D>2 proposed by E. Verlinde.