Probing the Thermodynamic Phase Structure of Black Holes through Euler characteristic

TL;DR

This paper investigates the topological structure of black hole thermodynamics using Euler characteristic across different geometries, revealing how microscopic interactions influence phase transitions and stability.

Contribution

It introduces a novel approach linking thermodynamic topology with geometry to analyze black hole phase structures and interactions.

Findings

Euler characteristic signals phase transitions.

Interactions increase near the spinoidal curve.

Topological changes reflect stabilization in new phases.

Abstract

In this work, we attempt to explore a possible connection between thermodynamic topology and the thermodynamic geometry formulation of black hole thermodynamics. We study the topological structure of black hole thermodynamic phase spaces by calculating the Euler characteristic (EC) using four well-known thermodynamic geometries: Weinhold, Ruppeiner, Geometrothermodynamics (GTD), and HPEM. We interpret the Euler characteristic as an indicator of the degree of microscopic interactions within the thermodynamic system. As the system approaches the spinoidal curve, the interaction strength increases significantly, eventually driving a phase transition. Beyond the spinoidal region, the interactions begin to weaken, and the system gradually stabilizes into a new phase configuration, reflected by a corresponding change in the topological structure of the thermodynamic state space.