Classical resolution of black hole singularities in arbitrary dimension

TL;DR

This paper demonstrates that in higher-dimensional modified gravity theories using a metric-affine approach, black hole singularities can be classically resolved through second-order field equations, with implications for AdS/CFT correspondence.

Contribution

It shows that metric-affine formulations yield always second-order field equations in higher dimensions, unlike standard metric approaches, and applies this to Born-Infeld gravity to resolve black hole singularities.

Findings

Second-order field equations are always obtained in the metric-affine approach.

Exact electrovacuum solutions in Born-Infeld gravity are derived.

Black hole singularities can be classically resolved in arbitrary dimensions.

Abstract

A metric-affine approach is employed to study higher-dimensional modified gravity theories involving different powers and contractions of the Ricci tensor. It is shown that the field equations are \emph{always} second-order, as opposed to the standard metric approach, where this is only achieved for Lagrangians of the Lovelock type. We point out that this property might have relevant implications for the AdS/CFT correspondence in black hole scenarios. We illustrate these aspects by considering the case of Born-Infeld gravity in $d$ dimensions, where we work out exact solutions for electrovacuum configurations. Our results put forward that black hole singularities in arbitrary dimensions can be cured in a purely classical geometric scenario governed by second-order field equations.