New solutions of exotic charged black holes and their stability

TL;DR

This paper introduces new charged black hole solutions in third order Lovelock Gravity with exotic horizons, analyzing their thermodynamics and stability, revealing phase transitions and conditions for extremal black holes.

Contribution

It presents a novel class of charged black hole solutions with non-constant curvature horizons in Lovelock Gravity, including stability and thermodynamic analysis.

Findings

Existence of extremal black holes with zero or positive Ricci scalar horizons.

Phase transition between small and very small black holes from stable to unstable.

Large black holes are stable against fluctuations.

Abstract

We find a class of charged black hole solutions in third order Lovelock Gravity. To obtain this class of solutions, we are not confined to the usual assumption of maximal symmetry on the horizon and will consider the solution whose boundary is Einstein space with supplementary conditions on its Weyl tensor. The Weyl tensor of such exotic horizons exposes two charge-like parameter to the solution. These parameters in addition with the electric charge, cause different features in compare with the charged solution with constant-curvature horizon. For this class of asymptotically (A)dS solutions, the electric charge dominates the behavior of the metric as r goes to zero, and thus the central singularity is always timelike. We also compute the thermodynamic quantities for these solutions and will show that the first law of thermodynamics is satisfied. We also show that the extreme black holes with nonconstant-curvature horizons whose Ricci scalar are zero or a positive constant could exist depending on the value of the electric charge and charged-like parameters. Finally, we investigate the stability of the black holes by analyzing the behavior of free energy and heat capacity specially in the limits of small and large horizon radius. We will show that in contrast with charged solution with constant-curvature horizon, a phase transition occurs between very small and small black holes from a stable phase to an unstable one, while the large black holes show stability to both perturbative and non-perturbative fluctuations.