Phase transitions and Geometrothermodynamics of Regular black holes

TL;DR

This paper explores the thermodynamic phase transitions and geometric properties of various regular black holes, revealing second order phase transitions and singularities through heat capacity and geometrothermodynamics analysis.

Contribution

It applies geometrothermodynamics to identify phase transition singularities in several regular black hole solutions, extending understanding of their thermodynamic behavior.

Findings

All studied black holes exhibit second order thermodynamic phase transitions.

Discontinuities in heat capacity and cusp points in free energy indicate phase transitions.

Curvature scalar analysis confirms thermodynamic singularities.

Abstract

In this paper we study the thermodynamics and state space geometry of regular black hole solutions such as Bardeen black hole, Ay\'{o}n-Beato and Garc\'{i}a black hole, Hayward black hole and Berej-Matyjasek-Trynieki-Wornowicz black hole. We find that all these black holes show second order thermodynamic phase transitions(SOTPT) by observing discontinuities in heat capacity-entropy graphs as well as the cusp type double point in free energy-temperature graph. Using the formulation of geometrothermodynamics we again find the singularities in the heat capacity of the black holes by calculating the curvature scalar of the Legendre invariant metric.