On the regularity of deformed extremal horizons

TL;DR

The paper reconsiders the regularity of extremal horizons under scalar perturbations, focusing on extremal RN–AdS black holes and exploring non-spherical deformations. It demonstrates that individual components of the scalar stress-energy tensor may diverge in some coordinates, yet the total backreaction and curvature invariants remain finite within perturbation theory, and identifies a horizon-regularity constraint that enables smooth crossing of null geodesics. The work shows that a broad class of locally regular, non-spherical extremal horizons can arise and may be realized by physically reasonable sources, including scalar fields and PD-type metrics, while unconstrained deformations generally lead to geodesic incompleteness. These findings argue against the notion that extremal horizons universally amplify ultraviolet effects and instead point to a nuanced landscape where horizon regularity depends on geometric constraints and the matter content near the horizon.

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--Nordström 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.