Legendre transformations and the thermodynamic geometry of 5D black holes

TL;DR

This paper explores the thermodynamic geometry of 5D black holes in Einstein-Gauss-Bonnet gravity, demonstrating that Legendre invariant metrics accurately reflect phase transitions and thermodynamic interactions.

Contribution

It introduces Legendre invariant metrics in geometrothermodynamics to analyze 5D black holes, linking curvature scalar to phase transition points.

Findings

Legendre invariant metrics reproduce thermodynamic behavior.

Curvature scalar indicates phase transition points.

Both Einstein-Yang-Mills-Gauss-Bonnet and Einstein-Maxwell-Gauss-Bonnet theories are analyzed.

Abstract

This paper studies the thermodynamic properties of the 5D black hole in Einstein-Gauss-Bonnet gravity from the viewpoint of geometrothermodynamics. It {is found} that the Legendre invariant metrics of the 5D black {holes} in Einstein-Yang-Mills-Gauss-Bonnet {theory and} Einstein-Maxwell-Gauss-Bonnet {theory} reproduce the behavior of the thermodynamic interaction and phase transition structure of the corresponding black hole configurations {correctly}. It is shown that they are both curved and {that} the curvature scalar {provides} information about the phase transition point.