D-dimensional Bardeen\u2013AdS black holes in Einstein\u2013Gauss\u2013Bonnet theory

Abstract

We present a D-dimensional Bardeen like Anti-de Sitter (AdS) black hole solution in Einstein–Gauss–Bonnet (EGB) gravity, viz., Bardeen–EGB–AdS black holes. The Bardeen–EGB–AdS black hole has an additional parameter due to magnetic charge (e), apart from mass (M) and Gauss–Bonnet parameter (alpha ). Interestingly, for each value of alpha , there exist a critical e = e_E which corresponds to an extremal regular black hole with degenerate horizons, while for e< e_E, it describes non-extremal black hole with two horizons. Despite the complicated solution, the thermodynamical quantities, like temperature (T), specific heat(C) and entropy (S) associated with the black hole are obtained exactly. It turns out that the heat capacity diverges at critical horizon radius r_+ = r_C, where the temperature attains maximum value and the Hawking-Page transition is achievable. Thus, we have an exact D-dimensional regular black holes, when evaporates lead to a thermodynamical stable remnant.