Exactd-dimensional Bardeen-de Sitter black holes and thermodynamics

Abstract

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 $\ensuremath{\mu}={\ensuremath{\mu}}_{E}$, which corresponds to an extremal black hole when Cauchy and event horizons coincide, which for $\ensuremath{\mu}g{\ensuremath{\mu}}_{E}$ describes a nonextremal black hole with two horizons and no black hole for $\ensuremath{\mu}l{\ensuremath{\mu}}_{E}$. We also find that the extremal value ${\ensuremath{\mu}}_{E}$ 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 ${C}_{e}g(l)0$. The Hawking evaporation of black holes leads to a thermodynamically stable double-horizon black hole remnant with the vanishing temperature.