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

TL;DR

This paper explores the complex phase structure and stability of charged black holes in third-order Lovelock gravity with nonconstant curvature horizons, revealing rich thermodynamic behaviors and phase transitions influenced by electromagnetic fields.

Contribution

It introduces the most general charged black hole solutions in third-order Lovelock gravity with nonconstant-curvature horizons and analyzes their thermodynamic stability and phase transitions.

Findings

Identified first- and second-order phase transitions including van der Waals-like behavior.

Demonstrated the influence of Lovelock corrections and electromagnetic fields on black hole stability.

Revealed the impact of conserved charges on black hole evaporation and stabilization.

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.