Recovery of consistency in thermodynamics of regular black holes in Einstein's gravity coupled with nonlinear electrodynamics

TL;DR

This paper investigates the thermodynamics of regular black holes in Einstein's gravity coupled with nonlinear electrodynamics, revealing a consistent phase transition description and confirming the Bekenstein-Hawking entropy formula.

Contribution

It introduces a revised thermodynamic phase space for regular black holes, ensuring the first law holds and phase transitions are accurately described.

Findings

The Maxwell equal area law applies during phase transitions.

Entropy follows the Bekenstein-Hawking area law.

A complete phase transition process is characterized by the new equation of state.

Abstract

As one of candidate theories in the construction of regular black holes, Einstein's gravity coupled with nonlinear electrodynamics has been a topic of great concerns. Owing to the coupling between Einstein's gravity and nonlinear electromagnetic fields, we need to reconsider the first law of thermodynamics, which will lead to a new thermodynamic phase space. In such a phase space, the equation of state accurately describes the complete phase transition process of regular black holes. The Maxwell equal area law strictly holds when the phase transition occurs, and the entropy obeys the Bekenstein-Hawking area formula, which is compatible with the situation in Einstein's gravity.