| Summary: | 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, 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 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.
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