On the regularity of deformed extremal horizons

TL;DR

This paper investigates the regularity and geometric properties of non-spherical extremal black holes, showing that certain divergences do not lead to physical singularities and identifying conditions for smooth horizon crossing.

Contribution

It demonstrates that non-spherical extremal Reissner–Nordström AdS black holes can have regular horizons despite some divergences, expanding understanding of horizon regularity.

Findings

Certain stress-energy tensor components diverge but do not cause singularities.

Null geodesics can cross the horizon smoothly under specific geometric conditions.

A broad class of spacetimes with regular non-spherical horizons exists.

Abstract

It has recently been argued that extremal black holes can act as amplifiers of new physics, due to horizon instabilities that enhance the effects of ultraviolet corrections. In this paper, we revisit some of these claims and investigate the viability of a class of non-spherical extremal black holes. In particular, we revisit the regularity of perturbed extremal Reissner--Nordstr\"om AdS black holes showing that, while some certain components of the scalar stress energy tensor diverge, the backreaction remains finite. We also study geodesic completeness, identifying a simple geometric constraint which, if satisfied, ensures that null geodesics cross the horizon smoothly. This analysis suggests the existence of a broad class of spacetimes with regular non-spherical horizons.