Conventional vs. modified GTD metrics: Survival of modified GTD metrics in AdS spacetime and thermodynamic ensembles

TL;DR

This paper investigates the robustness of modified Geometrothermodynamics (GTD) metrics in AdS black hole thermodynamics, demonstrating their consistent ability to encode physical boundaries across different spacetime backgrounds and thermodynamic ensembles.

Contribution

It extends the applicability of modified GTD metrics to AdS spacetime and various thermodynamic ensembles, confirming their universality and physical relevance.

Findings

Modified GTD metrics respect thermodynamic phase space boundaries.

Behavior of modified GTD metrics is consistent in AdS spacetime.

Modified GTD metrics are invariant under Legendre transformations.

Abstract

Thermodynamic geometry provides a powerful framework for probing the microscopic structure of thermodynamic systems. Among its formulations, Geometrothermodynamics (GTD) has been widely applied to black hole thermodynamics, owing to its Legendre-invariant construction. However, recent work has shown that conventional GTD metrics fail to encode essential physical boundaries of thermodynamic phase space. By modifying the conventional metric structure, three new GTD metrics were previously introduced, which successfully capture these boundaries in regular spacetime. Whether such modified metrics remain viable in different spacetime backgrounds and under changes of thermodynamic ensemble has remained an open question. In this work, I address this issue by investigating the behavior of modified GTD metrics in AdS spacetime and across different thermodynamic ensembles in the framework of Bardeen AdS black hole. An analysis of thermodynamic geodesics demonstrates that the modified GTD metrics consistently respect physical boundaries of the phase space, in contrast to conventional GTD metrics. This behavior is preserved in AdS spacetime and under Legendre transformations, establishing the robustness and universality of the modified GTD framework.