Evolution and endpoint of the black string instability: Large D solution

TL;DR

This paper derives simplified equations to model the evolution of black strings in high dimensions, demonstrating their instability and eventual transition to stable non-uniform configurations, confirming previous conjectures.

Contribution

It introduces a new set of solvable PDEs for black string dynamics at large D, revealing the instability process and endpoint configurations.

Findings

Thin black strings are unstable to inhomogeneities.

Unstable strings evolve into stable non-uniform black strings.

Final configurations resemble arrays of localized black holes.

Abstract

We derive a simple set of non-linear, (1+1)-dimensional partial differential equations that describe the dynamical evolution of black strings and branes to leading order in the expansion in the inverse of the number of dimensions D. These equations are easily solved numerically. Their solution shows that thin enough black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to stable non-uniform black strings. This proves an earlier conjecture about the endpoint of the instability of black strings in a large enough number of dimensions. If the initial black string is very thin, the final configuration is highly non-uniform and resembles a periodic array of localized black holes joined by short necks. We also present the equations that describe the non-linear dynamics of Anti-deSitter black branes at large D.