Bardeen-like regular black holes in $5D$ 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 additional parameter $g$ 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 $r=r_C$, 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 extremel black hole remnants with vanishing temperature. The heat capacity becomes positive $C_{+}>0$ for $r_{+}<r_C$ 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 area $A$, i.e., $S\ne A/4$.

arXiv comment20 pages, 7 figures

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