2D Black Holes, Conformal Vacua and CFTs on the Cylinder

TL;DR

This paper explores 2D dilaton gravity models with power-law potentials, revealing their black hole solutions' conformal properties and linking their thermodynamics to 2D CFTs on the cylinder.

Contribution

It demonstrates the conformal transformation laws of these models' ground states and connects black hole thermodynamics to 2D conformal field theories.

Findings

Ground states obey SL(2,R) conformal transformations.

Black hole entropy matches 2D CFT predictions.

Thermodynamical parameters exhibit scaling behavior.

Abstract

We investigate two-dimensional dilaton gravity models with a power-law dilaton potential, whose black hole solutions contain, among others, the dimensional reduction of the Schwarzschild black hole, the Anti-de Sitter black hole and Rindler spacetime. We show that the ground state of these models satisfies simple transformation laws under the SL(2,R) conformal group. We use these transformation laws to explain the scaling behavior of the thermodynamical parameters of the black hole and the nonextensivity of the thermodynamical system. The black hole thermodynamical behavior, in particular its entropy, is reproduced by a mapping into a two-dimensional conformal field theory on the cylinder.