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.
On Brane Instabilities in the Large $D$ Limit
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abstract
Using an expansion in large number of dimensions, taken to subleading orders, we discuss several issues concerning the Gregory-Laflamme instabilities. We map out the phase diagram of neutral and charged black strings, and comment on the possible transition in the nature of the final state of the instability at higher order in the 1/D expansion. We also discuss unstable black membranes, and show that in certain limits the preferred shape of the non-uniform phase is a triangular lattice.
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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.