Exact d -dimensional Bardeen-de Sitter black holes and thermodynamics

The Bardeen metric is the first spherically symmetric regular black hole solution of Einstein's equations coupled to nonlinear electrodynamics, which has an additional parameter (e ) due to nonlinear charge apart from mass (M ). We find a d -dimensional Bardeen-de Sitter black hole and analyze its horizon structure and thermodynamical properties. Interestingly, in each spacetime dimension d , there exists a critical mass parameter μ =μ_E, which corresponds to an extremal black hole when Cauchy and event horizons coincide, which for μ >μ_E describes a nonextremal black hole with two horizons and no black hole for μ <μ_E. We also find that the extremal value μ_E is influenced by the spacetime dimension d . Owing to the nonlinear charge corrected metric, the thermodynamic quantities of the black holes also get modified and a Hawking-Page-like phase transition exists. The phase transition is characterized by a divergence of the heat capacity at a critical radius r₊=r_+C, with the stable (unstable) branch for C_e>(<)0 . The Hawking evaporation of black holes leads to a thermodynamically stable double-horizon black hole remnant with the vanishing temperature.