Taming the Aretakis instability: extremal black holes with multi-degenerate horizons

TL;DR

This paper explores the Aretakis instability in extremal black holes with degenerate horizons, showing it weakens with higher degeneracy and proposing a stable infinitely degenerate horizon geometry.

Contribution

It demonstrates the weakening of Aretakis instability with increasing horizon degeneracy and introduces a new stable black hole geometry with an infinitely degenerate horizon.

Findings

Aretakis instability diminishes as horizon degeneracy increases.

Proposed geometry with infinitely degenerate horizon is stable under Aretakis perturbations.

Potential new end state for extremal black holes with stable horizons.

Abstract

Stationary black hole geometries with non-degenerate Cauchy horizons are classically unstable due to mass inflation. At extremality, mass inflation is absent, but a different dynamical instability arises: the Aretakis instability. In this work, we investigate the properties of degenerate horizons and their associated Aretakis instabilities. By studying examples with increasingly higher-order horizon degeneracy, we show that the Aretakis instability weakens as the degree of degeneracy grows. Motivated by these results, we propose a new black hole geometry characterized by an infinitely degenerate horizon, which we argue is stable under Aretakis-type perturbations and may therefore provide a concrete realization of a "graveyard" end state for these objects.