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 $\mu ={\mu }_E$, which corresponds to an extremal black hole when Cauchy and event horizons coincide, which for $\mu >{\mu }_E$ describes a nonextremal black hole with two horizons and no black hole for $\mu <{\mu }_E$. We also find that the extremal value ${\mu }_E$ 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.

• Received 26 January 2018

DOI:https://doi.org/10.1103/PhysRevD.98.084025