Charged Black Holes in Quasi-Topological Gravity Coupled to Born-Infeld Nonlinear Electrodynamics

TL;DR

This paper constructs and analyzes static charged black hole solutions in quasi-topological gravity coupled with Born-Infeld nonlinear electrodynamics, revealing conditions for regularity and core structure changes.

Contribution

It provides explicit closed-form solutions for charged black holes in this combined gravity-electrodynamics framework, including regularity conditions and core structure modifications.

Findings

Charged black holes can be regular or singular depending on the model.

In some models, the interior core shifts from de Sitter to anti-de Sitter.

Explicit solutions involve hypergeometric functions.

Abstract

We construct static, spherically symmetric black hole solutions in quasi-topological gravity (QTG) coupled to Born-Infeld nonlinear electrodynamics. Starting from the spherically reduced action, we derive closed-form expressions for the electric field, the nonlinear Lagrangian, and the metric function, the latter involving hypergeometric functions. We consider specific versions of QTG in which vacuum black holes are regular, and show that, for some of these models, charged black holes develop a curvature singularity at a finite radius in their interior. In contrast, in models such as a Born-Infeld-type QTG, charged black holes remain regular. In this case, however, the de Sitter core of the neutral solution is replaced by an anti-de Sitter core. We also discuss several limiting regimes of these solutions.