Black Hole Thermodynamics in Carath\'eodory's Approach

TL;DR

This paper applies Carathéodory's thermodynamic approach to black holes, revealing a quasi-homogeneity symmetry in the Pfaffian form that enables the calculation of an integrating factor and the thermodynamic foliation of Kerr-Newman black holes.

Contribution

It demonstrates how Carathéodory's framework can be used to analyze black hole thermodynamics through quasi-homogeneity symmetry.

Findings

Identification of quasi-homogeneity symmetry in black hole thermodynamics

Calculation of an integrating factor for the Pfaffian form

Recovery of the thermodynamic foliation of Kerr-Newman black holes

Abstract

We show that, in the framework of Carath\'eodory's approach to thermodynamics, one can implement black hole thermodynamics by realizing that there exixts a quasi-homogeneity symmetry of the Pfaffian form $\deq$ representing the infinitesimal heat exchanged reversibly by a Kerr-Newman black hole; this allow us to calculate readily an integrating factor, and, as a consequence, a foliation of the thermodynamic manifold can be recovered.