Taming the Aretakis instability: extremal black holes with multi-degenerate horizons
Shreyansh Agrawal, Panagiotis Charalambous, Laura Donnay, Stefano Liberati, Giulio Neri
TLDR
This paper shows that Aretakis instability in extremal black holes weakens with increasing horizon degeneracy, proposing a stable, infinitely degenerate black hole.
Key contributions
- Investigates Aretakis instability in extremal black holes with degenerate horizons.
- Demonstrates that Aretakis instability weakens as horizon degeneracy increases.
- Proposes a novel black hole geometry featuring an infinitely degenerate horizon.
- Suggests this new geometry is stable against Aretakis perturbations, a potential "graveyard" state.
Why it matters
Extremal black holes face the Aretakis instability, posing a challenge to their long-term stability. This research offers a potential solution by proposing a new, infinitely degenerate black hole geometry. This could represent a stable, final "graveyard" state for these objects, advancing our understanding of black hole evolution.
Original 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.
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