Thermodynamic Geometry of the Born-Infeld-anti-de Sitter black holes

TL;DR

This paper applies thermodynamic geometry to four-dimensional Born-Infeld-anti-de Sitter black holes, analyzing scalar curvatures and divergences, revealing differences from traditional heat capacity analysis and exploring Legendre invariance.

Contribution

It introduces the application of thermodynamic geometry to BIAdS black holes, comparing different metrics and their divergence points, highlighting novel geometric insights.

Findings

Scalar curvature singularities differ from heat capacity singularities.

Davies points coincide with divergences of Legendre-invariant metrics.

Different thermodynamic metrics reveal distinct geometric structures.

Abstract

Thermodynamic geometry is applied to the Born-Infeld-anti-de Sitter black hole (BIAdS) in the four dimensions, which is a nonlinear generalization of the Reissner-Norstr\"Aom-AdS black hole (RNAdS). We compute the Weinhold as well as the Ruppeiner scalar curvature and find that the singular points are not the same with the ones obtained using the heat capacity. Legendre-invariant metric proposed by Quevedo and the metric obtained by using the free energy as the thermodynamic potential are obtained and the corresponding scalar curvatures diverge at the Davies points.