Non-spherically symmetric black string perturbations in the large D limit

TL;DR

This paper analyzes non-spherical perturbations of black strings in the large D limit, proving stability for most modes and confirming the Gregory-Laflamme instability as the only instability.

Contribution

It introduces a simplified analytical framework for black string perturbations in large D, proving stability for a broad class of modes and confirming the uniqueness of the Gregory-Laflamme instability.

Findings

No instabilities for most non-spherical perturbations in large D

All non-spherical static perturbations are stable

The Gregory-Laflamme instability is the only instability present

Abstract

We consider non-spherically symmetric perturbations of the uncharged black string/flat black brane in the large dimension (D) limit of general relativity. We express the perturbations in a simplified form using variables introduced by Ishibashi and Kodama. We apply the large D limit to the equations, and show that this leads to decoupling of the equations in the near-horizon and asymptotic regions. It also enables use of matched asymptotic expansions to obtain approximate analytical solutions and to analyze stability of the black string/brane. For a large class of non-spherically symmetric perturbations, we prove that there are no instabilities in the large D limit. For the rest, we provide additional matching arguments that indicate that the black string/brane is stable. In the \emph{static} limit, we show that for \emph{all} non-spherically symmetric perturbations, there is no instability. This is proof that the Gross-Perry-Yaffe mode for semiclassical black hole perturbations is the unique unstable mode even in the large D limit. This work is also a direct analytical indication that the only instability of the black string is the Gregory-Laflamme instability.