On AdS Black Strings at Large $D$

TL;DR

This paper investigates the stability of homogeneous AdS black strings with scalar fields at large dimensions, showing that nonlinear dynamics favor uniform solutions and that certain instabilities are suppressed at late times.

Contribution

It introduces a large D effective theory approach to analyze the nonlinear stability of AdS black strings with scalar fields, revealing the dominance of uniform solutions.

Findings

Nonlinear evolution favors uniform black string solutions.

Gregory-Laflamme instability is suppressed at late times.

Large D expansion simplifies stability analysis.

Abstract

In this paper we study the stability of an homogeneous black string in the presence of a negative cosmological constant with minimally coupled scalar fields by using the large $D$ effective theory. This method allows us to explore the dynamics of the black strings in the nonlinear regime. We find that up to the next-to-leading order of the $1/D$ expansion, the unique consistent solution of the equations of motion must be uniform. This means the recently found Gregory-Laflamme instability caused by fined-tuned non-generic perturbations would die out at late time in the evolution of the system.