Thermodynamic Geometry and Topological Einstein–Yang–Mills Black Holes

Stefano Bellucci,Bhupendra Nath Tiwari

doi:10.3390/e14061045

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 Weinhold surface of higher dimensional gravity, 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 ≥ 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 extremal Einstein–Yang–Mills black holes.

Highlights

For the given vacuum parameters, we shall exhibit that the parametric thermodynamic geometry is well capable to describe the perspective statisticalstability corresponding to the topological Einstein–Yang–Mills black hole configurations
The thermodynamic geometric analysis of the topological Einstein–Yang–Mills black hole configurations is offered under the fluctuations of the vacuum parameters, namely the electric charge and the cosmological constant
The thermodynamic geometric procedure is presented for the black holes carrying a (i) cosmological constant term and (ii) an electric charge

Summary

Introduction

Thermodynamic geometry [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] plays important role in understanding the stability and phase structure properties of black holes. For given (n + 1)-dimensional topological Einstein–Yang–Mills black holes with a negative cosmological constant, the thermodynamics lies on the properties of the Einstein field equations, gauge current and stress-energy tensor for arbitrary finite semi-simple gauge group. It is worth mentioning that the notion of the thermodynamic geometry opens new direction to examine the stability properties of topological Einstein–Yang–Mills black holes in arbitrary (n + 1)-dimensional space-time with SO(n(n − 1)/2 − 1, 1) semi-simple gauge group symmetries. From the perspective of the thermodynamic geometries and fluctuation theory, the statistical ensemble (in)stabilities via the Ruppeiner geometry and the corresponding Legendre transformed Weinhold geometry of the arbitrary finite space-time dimensional topological Einstein–Yang–Mills black hole configurations are of the particular interest in the consideration of the present paper.

Thermodynamic Geometry

Ruppeiner Geometry

Five Dimensional Black Holes

Higher Dimensional Black Holes

Weinhold Geometry

Conclusions