Fan-Wang type regular black holes in Quasi-Topological Gravity

TL;DR

This paper introduces a new class of regular black hole solutions in higher-dimensional quasi-topological gravity, achieved through higher-curvature corrections without matter fields, and demonstrates their regularity even for negative mass cases.

Contribution

It generalizes Fan-Wang regular black holes to higher dimensions within quasi-topological gravity, avoiding matter fields and explicitly determining the necessary coupling constants.

Findings

Solutions are asymptotically flat with regular centers.

Regularity persists even for negative mass black holes.

Higher-curvature terms replace matter fields in regular black hole construction.

Abstract

We construct a class of regular black hole solutions of the Fan-Wang type within quasi-topological gravity (QTG) in arbitrary spacetime dimensions greater than four. In contrast to the original Fan-Wang solution, which was obtained in four-dimensional general relativity coupled to nonlinear electrodynamics, our higher-dimensional generalization does not require any matter fields. Instead, regularity is achieved purely through an infinite tower of higher-curvature corrections. We demonstrate that the Fan-Wang-type metric is a solution to the QTG field equations by explicitly determining the corresponding coupling constants for each curvature order. Within an appropriate parameter regime, the solution describes an asymptotically flat black hole spacetime with a regular center. Remarkably, even in the case of negative mass, the geometry can remain completely regular, in sharp contrast to Einstein gravity.