Origin of black string instability

TL;DR

This paper investigates the classical Gregory-Laflamme instability in black strings, analyzing various gravitational perturbations to understand its origin and implications for stability conjectures.

Contribution

It provides a comprehensive classification of perturbations and demonstrates that the GL instability is the only normalizable negative mode among them.

Findings

The GL mode is the only negative mode indicating instability.

No other perturbations exhibit normalizable negative modes.

The study clarifies the origin of the black string instability.

Abstract

It is argued that many nonextremal black branes exhibit a classical Gregory-Laflamme (GL) instability. Why does the universal instability exist? To find an answer to this question and explore other possible instabilities, we study stability of black strings for all possible types of gravitational perturbation. The perturbations are classified into tensor-, vector-, and scalar-types, according to their behavior on the spherical section of the background metric. The vector and scalar perturbations have exceptional multipole moments, and we have paid particular attention to them. It is shown that for each type of perturbations there is no normalizable negative (unstable) modes, apart from the exceptional mode known as s-wave perturbation which is exactly the GL mode. We discuss the origin of instability and comment on the implication for the correlated-stability conjecture.