Generating Kerr-anti-de Sitter thermodynamics

TL;DR

This paper explores various thermodynamic descriptions of Kerr-anti-de Sitter black holes, introducing geometric methods to generate consistent thermodynamics that satisfy fundamental laws and extend to higher dimensions.

Contribution

It presents a novel geometric approach using iso-homogeneous transformations to construct thermodynamics satisfying the Smarr formula and first law for KadS black holes.

Findings

New thermodynamic frameworks satisfying the first law

Extension of thermodynamics to higher dimensions

Improved thermodynamic theory over Hawking's approach

Abstract

In the present work we study the construction of different thermodynamic descriptions for the Kerr-anti-de Sitter (KadS) black holes. The early versions of the KadS thermodynamics are briefly discussed, highlighting some of its strong points and shortcomings. Isohomogeneous transformations, a procedure for generating new thermodynamics, are presented and geometrically interpreted for KadS. This tool is used to determine possible KadS thermodynamics that can be constructed to satisfy a Smarr formula, and the validity of the first law in the generated thermodynamics. The connection between new thermodynamic theories and early Hawking's approach is considered. In this new framework, the usual KadS thermodynamics is complemented with its geometric construction, and Hawking's proposal, which does not satisfy the first law, is improved to an alternative thermodynamic theory. With the quantum statistical relation, Hawking's and this alternative KadS thermodynamics are also generalized from four to higher dimensions.