You've got a Freund--Rubin in Me: The Aretakis Instability of Extremal Black Branes

TL;DR

This paper studies the Aretakis instability in extremal black p-branes, linking its severity to near-horizon geometry and Kaluza-Klein spectra, revealing weaker instability than in extremal black holes but potential for worse singularities.

Contribution

It connects the Aretakis instability to the Kaluza-Klein spectrum of fields on Freund--Rubin spaces, providing a new way to analyze the instability's strength in black branes.

Findings

Aretakis instability exists in extremal black branes even without extra fields.

The instability's strength relates to the near-horizon AdS geometry and KK spectrum.

More modes can lead to increased curvature singularities compared to black holes.

Abstract

We investigate how the Aretakis instability affects non-dilatonic extremal black $p$-branes by focusing on their near-horizon geometry. Crucially, the strength of the instability, \textit{i.e.} the number of transverse derivatives needed to see non-decay/blow-up of fields on the horizon at late null time, is given by the scaling dimensions with respect to the near-horizon $\mathrm{AdS}_{p+2}$-factor. This renders the problem of determining the severity of the Aretakis instability equivalent to computing the Kaluza--Klein spectrum of fields on Freund--Rubin spaces. We use this to argue that non-dilatonic extremal black branes suffer from the Aretakis instability even in the absence of additional fields -- we find that this is weaker than for extremal black holes. We also argue that the scaling dimensions determine the smoothness of stationary deformations to the original black brane background -- here, our findings indicate that generically more modes can lead to worse curvature singularities compared to extremal black holes.