At large D, RN-dS and GB-dS black holes evolve to stationary lumpy solutions on the instability threshold, and in the unstable region their mass localizes into spot-like or ring-like configurations.
Small black holes in $AdS_5\times S^5$
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abstract
We consider small black holes in $AdS_5\times S^5$, smeared on $S^5$. We compute the spectrum of $\ell \in [1,10]$ $S^5$-quasinormal modes corresponding to fluctuations leading to localization of these black holes on $S^5$. We recover the zero mode found by Hubeny and Rangamani (HR) previously \cite{Hubeny:2002xn}, and explicitly demonstrate that a Gregory-Laflamme type instability is at play in this system. The instability is associated with the expectation value of a dimension-5 operator.
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The Fate of Instability of de Sitter Black Holes at Large $D$
At large D, RN-dS and GB-dS black holes evolve to stationary lumpy solutions on the instability threshold, and in the unstable region their mass localizes into spot-like or ring-like configurations.