Topologically nontrivial black holes in Lovelock-Born-Infeld gravity

TL;DR

This paper explores new black hole solutions in Lovelock gravity coupled with Born-Infeld electrodynamics, revealing unique horizon geometries, singularity structures, and stability behaviors influenced by nonlinear electromagnetic effects.

Contribution

It introduces black hole solutions with nonconstant-curvature horizons in Lovelock-Born-Infeld gravity, analyzing their singularities, thermodynamics, and stability, highlighting effects of nonlinear electrodynamics.

Findings

Existence of black holes with spacelike and timelike singularities.

Stability of large and small black holes with positive curvature.

Nonlinearity in electrodynamics affects black hole stability, especially at small Born-Infeld parameters.

Abstract

We present the black hole solutions possessing horizon with nonconstant-curvature and additional scalar restrictions on the base manifold in Lovelock gravity coupled to Born-Infeld (BI) nonlinear electrodynamics. The asymptotic and near origin behavior of the metric is presented and we analyze different behaviors of the singularity. We find that, in contrast to the case of the black hole solutions of BI-Lovelock gravity with constant curvature horizon and Maxwell-Lovelock gravity with nonconstant horizon which has only timelike singularities, spacelike, and timelike singularities may exist for BI-Lovelock black holes with nonconstant curvature horizon. By calculating the thermodynamic quantities, we study the effects of nonlinear electrodynamics via the Born-Infeld action. Stability analysis shows that black holes with positive sectional curvature, k, possess an intermediate unstable phase and large and small black holes are stable. We see that while Ricci flat Lovelock-Born-Infeld black holes having exotic horizons are stable in the presence of Maxwell field or either Born Infeld field with large born Infeld parameter beta, unstable phase appears for smaller values of beta, and therefore nonlinearity brings in the instability.