On the ensemble dependence in black hole geometrothermodynamics

TL;DR

This paper explores how the thermodynamic properties and phase transition structures of Einstein-Maxwell-Gauss-Bonnet black holes depend on the choice of statistical ensemble, revealing limitations of certain thermodynamic metrics in black hole geometrothermodynamics.

Contribution

It demonstrates that phase transition structures vary with thermodynamic potential choice, challenging the use of partially Legendre invariant metrics in black hole thermodynamics.

Findings

Phase transition structures depend on thermodynamic potential choice.

Partially Legendre invariant metrics are insufficient for describing black hole thermodynamics.

The study clarifies the limitations of current thermodynamic metrics in black hole analysis.

Abstract

We investigate the dependence of thermodynamic properties of black holes on the choice of statistical ensemble for a particular class of Einstein-Maxwell-Gauss-Bonnet black holes with cosmological constant. We use partial Legendre transformations in the thermodynamic limit in order to compare the results in different ensembles, and show that the phase transition structure depend on the choice of thermodynamic potential. This result implies that thermodynamic metrics which are partially Legendre invariant cannot be employed to describe black hole thermodynamics, and partly explains why a particular thermodynamic metric has been used so far in the framework of black hole geometrothermodynamics.