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

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