Phase transition of AdS black holes in 4D EGB gravity coupled to nonlinear electrodynamics

TL;DR

This paper investigates the phase transition and thermodynamic stability of AdS black holes in a regularized 4D Einstein-Gauss-Bonnet gravity coupled with nonlinear electrodynamics, revealing stable remnants and a secondary Hawking-Page transition.

Contribution

It provides exact solutions for NED-charged AdS black holes in 4D EGB gravity and analyzes their thermodynamics, including stability and phase transitions, which were not previously explored in this context.

Findings

Existence of thermodynamically stable black hole remnants.

Observation of a secondary Hawking-Page transition.

Modified entropy deviating from the area law.

Abstract

Einstein-Gauss-Bonnet (EGB) gravity is an outcome of quadratic curvature corrections to the Einstein-Hilbert gravity action in the form of a Gauss-Bonnet (GB) term in $ D > 4$ dimensions and EGB gravity is topologically invariant in $4D$. Recently several ways have been proposed for regularizing, a $ D \to 4 $ limit of EGB, for nontrivial gravitational dynamics in $ 4D $. Motivated by the importance of anti-de Sitter gravity/conformal field theory correspondence (AdS/CFT), we analyze black holes with AdS asymptotic to regularized $4D$ EGB gravity coupled to the nonlinear electrodynamics (NED) field. For a static spherically symmetric \textit{ansatz} the field equations are solved exactly, using two different approaches, for a NED Lagrangian to obtain an identical solution$-$namely NED charged AdS black holes in $4D$ EGB gravity which retains several known solutions. Owing to the NED charge corrected EGB black holes, the thermodynamic quantities are also modified, and the entropy does not obey the usual area law. We calculate the heat capacity and Helmholtz free energy, in terms of horizon radii, to investigate both local and global thermodynamic stability of black holes. We observe a secondary Hawking-Page transition between the smaller thermally favoured black hole and thermal AdS space. Our results show that the behaviour of Hawking's evaporation abruptly halts at shorter radii regime such that the black holes do have a thermodynamically stable remnant with vanishing temperature.