Geometrothermodynamics of Myers-Perry black holes

TL;DR

This paper explores the thermodynamics and Geometrothermodynamics of five-dimensional Myers-Perry black holes with varying angular momenta, revealing a consistent thermodynamic structure and phase transition indicators through geometric analysis.

Contribution

It applies Geometrothermodynamics to analyze black hole thermodynamics, uncovering phase transition signatures and stability changes in different angular momentum configurations.

Findings

Thermodynamic structure is fully captured by Geometrothermodynamics.

Singularities in curvature correspond to phase transitions.

Additional singularities indicate stability changes in the system.

Abstract

We consider the thermodynamics and Geometrothermodynamics of the Myers-Perry black holes in five dimensions for three different cases, depending on the values of the angular momenta. We follow Davies approach to study the thermodynamics of black holes and find a non-trivial thermodynamic structure in all cases, which is fully reproduced by the analysis performed with the techniques of Geometrothermodynamics. Moreover, we observe that in the cases when only one angular momentum is present or the two angular momenta are fixed to be equal, i.e. when the thermodynamic system is two dimensional, there is a complete agreement between the divergences of the generalized susceptibilities and the singularities of the equilibrium manifold, whereas when the two angular momenta are fully independent, that is, when the thermodynamic system is three dimensional, additional singularities in the curvature appear. However, we prove that such singularities are due to the changing from a stable phase to an unstable one.