Regular black holes in Einstein-Gauss-Bonnet gravity

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 (k > 0), that interpolates between the Boulware-Deser black hole (k = 0) and the Wiltshire charged black hole (r >> k). Owing to the appearance of the exponential correction factor (e(-k/r2)), 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.