Thermodynamic Geodesics in Bardeen Regular Black Hole: Conventional vs. Modified Geometrothermodynamics Metrics

TL;DR

This paper compares different thermodynamic metrics for Bardeen black holes, finds conventional metrics need modifications, and proposes improved metrics that better capture thermodynamic boundaries and properties.

Contribution

It introduces modified geometrothermodynamics metrics that more accurately reflect black hole thermodynamics compared to conventional metrics.

Findings

Modified metrics reveal thermodynamic boundaries like temperature vanishing and spinodal lines.

Modified metrics contain more thermodynamic information than conventional ones.

Modified metrics are most suitable for studying black hole thermodynamics.

Abstract

Thermodynamic geometry allow us to study the microscopic behavior of black hole system by defining a metric structure in thermodynamic phase space. Among the various thermodynamic metric structures, metrics defined by geometrothermodynamics (GTD) are extensively used to study the various thermodynamic system due to its Legendre invariant nature. In this work we investigate the behavior of thermodynamic geodesic of Bardeen regular black hole in thermodynamic space defined by three different GTD metrics. Based on the behavior of thermodynamic geodesic as well as thermodynamic curvature we argued that conventional GTD metric need some modifications to reflect all the thermodynamical properties of a system. We also modified the conventional GTD metrics and explore the behavior of thermodynamic geodesic defined by the modified metrics. Our study shows that the modified GTD metrics contain most of the information about the thermodynamical boundaries such as temperature vanishing line, spinodal line etc. of a black hole system. Based on the property of geodesic and Ricci scalar defined by the modified metrics we argued that the modified version of GTD metric are most suitable metric structures for studying the underlying thermodynamic behavior of a black hole system.