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

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 a number of 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 spherical symmetric \textit{ansatz} the field equations are solved exactly for a NED Lagrangian - 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 favored black hole and thermal AdS space. Our results show that the behavior of Hawking's evaporation abruptly halts at a smaller radii regime such that the black holes do have a thermodynamically stable remnant with vanishing temperature.