Thermodynamic Geometry and Topological Einstein-Yang-Mills Black Holes

TL;DR

This paper investigates the thermodynamic geometry and stability of topological Einstein-Yang-Mills black holes across various dimensions, providing criteria for their local and global statistical stability using geometric methods.

Contribution

It introduces a geometric framework to analyze the stability and fluctuations of Einstein-Yang-Mills black holes in arbitrary dimensions, extending previous thermodynamic studies.

Findings

Criteria for local stability derived from thermodynamic geometry.

Global stability conditions established for black hole ensembles.

Insights into fluctuation regimes and their statistical implications.

Abstract

From the perspective of the statistical fluctuation theory, we explore the role of the thermodynamic geometries and vacuum (in)stability properties for the topological Einstein-Yang-Mills black holes. In this paper, from the perspective of the state-space surface and chemical Wienhold surface, we provide the criteria for the local and global statistical stability of an ensemble of topological Einstein-Yang-Mills black holes in arbitrary spacetime dimensions $D\ge 5$. Finally, as per the formulations of the thermodynamic geometry, we offer a parametric account of the statistical consequences in both the local and global fluctuation regimes of the topological Einstein-Yang-Mills black holes.