Regular black holes in Einstein-Gauss-Bonnet gravity

Abstract

Einstein-Gauss-Bonnet theory, a natural generalization of general relativity to a higher dimension, admits a static spherically symmetric black hole which was obtained by Boulware and Deser. This black hole is similar to its general relativity counterpart with a curvature singularity at $r=0$. We present an exact 5D regular black hole metric, with parameter $(kg0)$, that interpolates between the Boulware-Deser black hole ($k=0$) and the Wiltshire charged black hole ($r\ensuremath{\gg}k$). Owing to the appearance of the exponential correction factor (${e}^{\ensuremath{-}k/{r}^{2}}$), responsible for regularizing the metric, the thermodynamical quantities are modified, and it is demonstrated that the Hawking-Page phase transition is achievable. The heat capacity diverges at a critical radius $r={r}_{C}$, where incidentally the temperature is maximum. Thus, we have a regular black hole with Cauchy and event horizons, and evaporation leads to a thermodynamically stable double-horizon black hole remnant with vanishing temperature. The entropy does not satisfy the usual exact horizon area result of general relativity.