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

TL;DR

The work addresses singularities in classical gravity by embedding a vacuum generalization of Fan–Wang regular black holes into higher-dimensional quasi-topological gravity, using an infinite tower of higher-curvature terms to mimic the regularizing effects of matter. By reconstructing the function $h(\psi)$ and fixing the couplings via a Lagrange inversion approach, the authors show that a Fan–Wang–type metric with a de Sitter core is a bona fide vacuum solution in $D>4$ for $\mu=3$ and $\nu=3\BAR{\nu}$, yielding an asymptotically flat spacetime with a regular center and a rich horizon structure. They compute the ADM mass, Wald entropy, and Hawking temperature within QT gravity, demonstrating thermodynamic consistency and identifying regimes with two horizons, an extremal horizon, or horizonless geometries, including the intriguing possibility of regular negative-mass spacetimes for even $\BAR{\nu}$. The results highlight how infinite higher-curvature corrections can drive singularity resolution without matter fields, offering a concrete framework for exploring quantum-gravity-inspired regular black holes in higher dimensions and their holographic implications.

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.