Thermodynamics of nonspherical black holes from Liouville theory

TL;DR

This paper refines a Liouville theory approach to describe the thermodynamics of various black holes, including nonspherical ones, by providing general formulas for temperature and entropy calculations.

Contribution

It extends the Liouville formalism to nonspherical black holes and offers a more advantageous method for calculating black hole entropy compared to previous Hamiltonian approaches.

Findings

Derived general formulas for black hole temperature from Liouville theory.

Extended the formalism to include nonspherical black holes like black rings and topological black holes.

Provided a more efficient method for entropy calculation using the Lagrangian approach.

Abstract

A Liouville formalism was proposed many years ago to account for the black hole entropy. It was recently updated to connect thermodynamics of general black holes, in particular the Hawking temperature, to two-dimensional Liouville theory. This relies on the dimensional reduction to two-dimensional black hole metric. The relevant dilaton gravity model can be rewritten as a Liouville-like theory. We refine the method and give general formulas for the corresponding scalar and energy-momentum tensors in Liouville theory. This enables us to read off the black hole temperature using a relation which was found about three decades ago. Then the range of application is extended to include nonspherical black holes such as neutral and charged black rings, topological black hole and the case coupled to a scalar field. As for the entropy, following previous authors, we invoke the Lagrangian approach to central charge by Cadoni and then use the Cardy formula. The general relevant parameters are also given. This approach is more advantageous than the usual Hamiltonian approach which was used by the old Liouville formalism for black hole entropy.