Anti-de Sitter Hayward black holes in Einstein–Gauss–Bonnet gravity

Abstract

Lovelock gravitation theory is a natural extension of the General Relativity to higher dimensions with the inclusion of only second-order terms correspond to the Einstein–Gauss–Bonnet gravity. In this paper, we find an exact Hayward black hole solution of D ≥ 5 -dimensional spacetime for Einstein–Gauss–Bonnet (EGB) gravity with negative cosmological constant ( Λ ) minimally coupled to non-linear electrodynamics for a specific Lagrangian density, namely, EGB-AdS black holes, with additional parameter e because of magnetic charge. Interestingly, it turns out that for each value of GB parameter ( α ) , there exist a critical e E such that for e < e E describe non-extremal black holes with Cauchy ( r − ) and Event horizons ( r + ), while for e = e E corresponds to an extremal regular black hole with degenerate horizons ( r + = r − = r E ). Owing to the magnetically charged corrected black hole, the thermodynamic quantities have also been modified, but the entropy does not satisfy the usual area law. A divergence of the specific heat at r + = r c , where the temperature attains maximum value and the Hawking–Page transition is achievable with the stable (unstable) branch for r t 1 ≤ r + < r c ( r c < r + ≤ r t 2 ). Thus, we found Hayward EGB-AdS black holes which do not evaporate completely, but lead to stable double-horizon black hole remnants with vanishing temperature and positive heat capacity.