Phase Transitions of Electromagnetically Charged Black Holes in Lovelock Gravity with Nonconstant Curvature Horizons

Abstract

We present the most general class of charged black hole solutions in third-order Lovelock gravity within even-dimensional spacetimes in the presence of an electromagnetic field. These solutions feature nonconstant-curvature horizons that affect geometry when n>=8. The near-origin behavior of the metric reveals a timelike singularity for electrically charged cases, in contrast to the spacelike singularity found in the uncharged case. We investigate thermodynamic stability in both the grand canonical and canonical ensembles. In the grand canonical ensemble, stability is determined by the positivity of both the Hessian determinant and the temperature. In the canonical ensemble, the sign of the heat capacity governs stability. We identify both first- and second-order phase transitions, including a van der Waals-like behavior characterized by instability at intermediate black hole sizes. Our results reveal a rich phase structure influenced by Lovelock corrections and electromagnetic fields, and demonstrate how conserved charges affect black hole evaporation and stabilization.