Geometrical thermodynamics and P-V criticality of the black holes with power-law Maxwell field

TL;DR

This paper explores the thermodynamical behavior and phase transitions of Einstein black holes with power Maxwell nonlinear electrodynamics, using geometrical thermodynamics and critical point analysis to understand stability and parameter effects.

Contribution

It introduces a geometrical thermodynamics framework for analyzing phase transitions in black holes with power Maxwell fields and derives critical values considering the cosmological constant as pressure.

Findings

Identification of phase transition points via geometrical thermodynamics

Analysis of parameter effects on black hole stability and thermodynamics

Calculation of thermodynamical quantities like volume expansion and sound speed

Abstract

We study thermodynamical structure of Einstein black holes in the presence of power Maxwell invariant nonlinear electrodynamics for two different cases. The behavior of the temperature and conditions regarding the stability of these black holes are investigated. Since the language of geometry is an effective method in general relativity, we concentrate on the geometrical thermodynamics to build a phase space for studying phase transition. In addition, taking into account the denominator of the heat capacity, we use the proportionality between cosmological constant and thermodynamical pressure to extract the critical values for these black holes. Besides, the effects of the variation of different parameters on thermodynamical structure of these black holes are investigated. In addition, some thermodynamical properties such as volume expansion coefficient, speed of sound and isothermal compressibility coefficient are calculated and some remarks regarding these quantities are given.