Vulnerability of Horizon Regularity: Horizon as a Natural Boundary

TL;DR

This paper investigates the stability of black hole horizons in extended Einstein gravity, revealing that irrational near-horizon expansions indicate the horizon as a natural boundary, with implications for quantum gravity theories.

Contribution

It demonstrates the inherent vulnerability of horizon regularity in Einstein gravity with higher curvature terms, especially in higher dimensions, and contrasts it with stable horizons in supergravity.

Findings

Irrational powers in near-horizon expansion imply horizon boundary nature.

Vulnerability occurs in higher dimensions, with some exceptions.

Supergravity theories preserve horizon regularity, unlike generic Einstein theories.

Abstract

We consider Einstein gravity extended with Riemann-squared term and construct the leading-order perturbative solution to the rotating black hole with all equal angular momenta in $D=7$. We find that in the extremal limit, the linear perturbation involves irrational powers in the near-horizon expansion. We argue that, despite that all curvature tensor invariants are regular on the horizon, the irrational power implies that the inside of the horizon is destroyed and the horizon becomes the natural boundary of the spacetime. We demonstrate that this vulnerability of the horizon regularity is an innate part of Einstein theory, and can arise in Einstein theory with minimally coupled matter. However, in fine-tuned theories such as supergravities, the black hole inside is preserved, which may be one of the criteria for a consistent theory of quantum gravity. We also show that the vulnerability occurs in general higher dimensions, which only a few sporadically distributed dimensions can evade.