On Brane Instabilities in the Large $D$ Limit

TL;DR

This paper investigates black string and membrane instabilities using large D expansions, revealing phase diagrams, potential transition behaviors, and preferred non-uniform shapes like triangular lattices.

Contribution

It provides a detailed analysis of Gregory-Laflamme instabilities at subleading orders in large D, offering new insights into phase transitions and geometric configurations.

Findings

Mapped phase diagram of black strings

Identified possible transition in instability final states

Found triangular lattice as preferred shape in certain limits

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.