Phase transition and thermodynamic geometry of Einstein-Maxwell-dilaton black holes

TL;DR

This paper investigates the phase transitions and thermodynamic geometry of Einstein-Maxwell-dilaton black holes, revealing multiple critical behaviors and proposing a new method to identify phase transitions through Ricci scalar analysis.

Contribution

It introduces a novel approach using thermodynamic geometry to effectively detect phase transitions in dilatonic black holes, extending the thermodynamic space with dilaton parameter.

Findings

Black holes exhibit two types of phase transitions depending on parameters.

Three critical behaviors are identified near phase transition points.

Ricci scalar behavior helps recognize phase transition types.

Abstract

In this paper, we consider a linearly charged dilatonic black holes and study their thermodynamical behavior in the context of phase transition and thermodynamic geometry. We show that, depending on the values of the parameters, these type of black holes may enjoy two types of phase transition. We also find that there are three critical behaviors near the critical points for these black holes; nonphysical unstable to physical stable, large to small, and small to large black holes phase transition. Next, we employ a thermodynamical metric for studying thermodynamical geometry of these black holes. We show that the characteristic behavioral of Ricci scalar of this metric enables one to recognize the type of phase transition and critical behavior of the black holes near phase transition points. Finally, we will extend thermodynamical space by considering dilaton parameter as extensive parameter. We will show that by this consideration, Weinhold, Ruppeiner and Quevedo metrics provide extra divergencies which are not related to any phase transition point whereas our new method is providing an effective machinery.