Charged Regular Black Holes From Quasi-topological Gravities in $D\ge 5$

TL;DR

This work tackles the singularity problem of black holes in $D \ge 5$ by employing quasi-topological gravity with an infinite tower of higher-curvature corrections to obtain charged static black holes. Through a reduction to an algebraic master equation for the metric, it is shown that with couplings $α_n$ chosen to be odd, nonnegative and to have a finite radius of convergence, the central singularity is cured in the infinite-order limit, producing an anti-de Sitter core. In $D=5$, explicit solutions are presented for correction orders $n=1$, $n=3$, and $n=\infty$, with only the infinite-order case yielding a globally regular spacetime and a finite Kretschmann scalar; the horizon structure is encoded by a parametric extremal curve, and the RN limit is recovered as $α \to 0$. The results indicate that infinite-order curvature corrections can regularize spacetime without exotic matter, offering a new mechanism relevant to quantum gravity effective actions and motivating further study of stability, thermodynamics, and rotating generalizations.

Abstract

The investigation of gravity in higher-dimensional spacetime has transitioned from a mathematical curiosity to a fundamental framework in theoretical physics, catalyzed by the dimensional requirements of String theory and M-theory. In this paper, we explicitly construct a spherically symmetric charged black hole solution in $D \ge 5$ dimensions within a gravity theory featuring an infinite tower of higher-curvature corrections. For a given mass and electric charge, the model admits a unique static spherically symmetric solution. We demonstrate that, with an appropriate choice of coupling coefficients $α_n$, the central singularity is progressively mitigated as the correction order increases, ultimately resolving into a globally regular spacetime in the limit of infinite-order corrections. Furthermore, the criteria for the existence of extremal black holes are determined.

Figures (4)

• Figure 1: The profiles of the metric function $f(r)$ for different correction orders $n = 1,3,\infty$, with the parameters fixed at $m=10$, $q=10$, and $\alpha=1$.
• Figure 2: The profiles of the metric function $f(r)$ for different correction orders $n = 1,3,\infty$, with the parameters fixed at $m=10$, $q=10$, and $\alpha=1$.
• Figure 3: Phase Diagram of 5D Charged Regular Black Holes ($\alpha=1$).
• Figure 4: The profiles of the Kretschmann scalar $K$ for correction orders $n =\infty$, with the parameters fixed at $q=10$, $\alpha=1$ and $m = 3, 6.4926, 8$.