Thermodynamic properties of Bardeen black holes in dRGT massive gravity

TL;DR

This paper explores the thermodynamic properties and stability of Bardeen black holes within dRGT massive gravity, revealing conditions for stability, phase transitions, and how the solution relates to Schwarzschild and standard Bardeen black holes.

Contribution

It introduces a new regular black hole solution in dRGT massive gravity and analyzes its thermodynamic behavior and stability, extending previous models.

Findings

Black hole solution reduces to Bardeen or Schwarzschild in specific limits.

Black hole is thermodynamically stable when heat capacity is positive.

Phase structure depends on horizon radius and ensemble type.

Abstract

The Bardeen black hole solution is the first spherically symmetric regular black hole based on the Sakharov and Gliner proposal which is a modification of the Schwarzschild black hole. We present the Bardeen black hole solution in the presence of the de Rham, Gabadaadze, and Tolly (dRGT) massive gravity, which is regular everywhere in the presence of a nonlinear source. The obtained solution reduces to the Bardeen black hole in the absence of a massive gravity parameter, and the Schwarzschild black hole when magnetic charge $g = 0$. We investigated the thermodynamic quantities, that is, mass (M), temperature $(T)$, entropy ($S$), and free energy $(F)$, in terms of the horizon radius for both canonical and grand canonical ensembles. We checked the local and global stability of the obtained solution by studying the heat capacity and free energy. The heat capacity changes sign at $r = r_c$. The black hole is thermodynamically stable with a positive heat capacity $C > 0$ (i.e., globally preferred with negative free energy $F < 0$). In addition, we studied the phase structure of the obtained solution in both ensembles.