Geometrothermodynamics in Horava-Lifshitz gravity

TL;DR

This paper explores the thermodynamic geometry of static, spherically symmetric black holes in Hořava-Lifshitz gravity, demonstrating that Legendre invariant metrics accurately reflect phase transitions and singularities.

Contribution

It introduces a Legendre invariant metric in geometrothermodynamics that correctly captures phase transitions in Hořava-Lifshitz black holes, including special limiting cases.

Findings

Legendre invariant metric reproduces phase transition structure

Curvature singularities correspond to thermodynamic limits

Analysis includes Einstein limit and flat horizon cases

Abstract

We investigate the thermodynamic geometries of the most general static, spherically symmetric, topological black holes of the Ho\v{r}ava--Lifshitz gravity. In particular, we show that a Legendre invariant metric derived in the context of geometrothermodynamics for the equilibrium manifold reproduces correctly the phase transition structure of these black holes. Moreover, the limiting cases in which the mass, the entropy or the Hawking temperature vanish are also accompanied by curvature singularities which indicate the limit of applicability of the thermodynamics and the geometrothermodynamics of black holes. The Einstein limit and the case of a black hole with flat horizon are also investigated.