Geometrothermodynamics of the Kehagias-Sfetsos Black Hole

TL;DR

This paper applies Legendre invariant geometrothermodynamics to the Kehagias-Sfetsos black hole, resolving previous anomalies by demonstrating the curvature singularity at phase transitions using the Quevedo metric.

Contribution

It shows that the Quevedo Legendre invariant metric correctly identifies phase transitions in the KS black hole, unlike Ruppeiner and Weinhold metrics, and explores potential potential choices.

Findings

Quevedo metric curvature is singular at phase transition points.

Ruppeiner metric does not show singularity at phase transitions.

Legendre invariance is crucial for consistent thermodynamic geometry analysis.

Abstract

The application of information geometric ideas to statistical mechanics using a metric on the space of states, pioneered by Ruppeiner and Weinhold, has proved to be a useful alternative approach to characterizing phase transitions. Some puzzling anomalies become apparent, however, when these methods are applied to the study of black hole thermodynamics. A possible resolution was suggested by Quevedo et al. who emphasized the importance of Legendre invariance in thermodynamic metrics. They found physically consistent results for various black holes when using a Legendre invariant metric, which agreed with a direct determination of the properties of phase transitions from the specific heat. Recently, information geometric methods have been employed by Wei et al. to study the Kehagias-Sfetsos (KS) black hole in Horava-Lifshitz gravity. The formalism suggests that a coupling parameter in this theory plays a role analogous to the charge in Reissner-Nordstrom (RN) black holes or angular momentum in the Kerr black hole and calculation of the specific heat shows a singularity which may be interpreted as a phase transition. When the curvature of the Ruppeiner metric is calculated for such a theory it does not, however, show a singularity at the phase transition point. We show that the curvature of a particular Legendre invariant ("Quevedo") metric for the KS black hole is singular at the phase transition point. We contrast the results for the Ruppeiner, Weinhold and Quevedo metrics and in the latter case investigate the consistency of taking either the entropy or mass as the thermodynamic potential.