Bardeen-like regular black holes in [formula omitted] Einstein–Gauss–Bonnet gravity

Abstract

We find an exact spherically symmetric regular Bardeen-like solutions by considering the coupling between Einstein-Gauss–Bonnet theory and nonlinear electrodynamics (NED) in five-dimensional spacetime. These solutions, with an additionalparameter g apart from the mass M, represent black holes with Cauchy and event horizons, extremal black holes with degenerate horizons or no black holes in the absence of the horizons, and encompasses as a special case Boulware-Deser black holes which can be recovered in the absence of magnetic charge ( g=0). Owing to the NED corrected black hole, the thermodynamic quantities have also been modified and we have obtained exact analytical expressions for the thermodynamical quantities such the Hawking temperature T+, the entropy S+, the specific heat C+, and the Gibbs free energy F+. The heat capacity diverges at a critical radius r=rC, where incidentally the temperature has a maximum, and the Hawking-Page transitions even in absence of the cosmological term. The thermal evaporation process leads to eternal remnants for sufficiently small black holes and evaporates to a thermodynamic stable extremal black hole remnants with vanishing temperature. The heat capacity becomes positive C+>0 for r+<rC allowing black hole to become thermodynamically stable, in addition the smaller black holes are globally stable with positive heat capacity C+>0 and negative free energy F+<0 . The entropy S of a 5D Bardeen black hole is not longer a quarter of the horizon’s area A, i.e., S≠A∕4.