The endpoint of the Gregory-Laflamme instability of black strings revisited

TL;DR

This study revisits the Gregory-Laflamme instability of black strings, confirming the horizon's self-similar evolution and finite-time pinch-off, which challenges cosmic censorship in higher-dimensional spacetimes.

Contribution

It extends previous work by analyzing black string evolution in five dimensions, confirming self-similar behavior and finite-time horizon pinch-off without a universal timescale.

Findings

Horizon evolves as a self-similar sequence of black strings

No evidence of a global timescale between generations

Horizon pinches off in finite asymptotic time

Abstract

We reproduce and extend the previous studies of Lehner and Pretorius of the endpoint of the Gregory-Laflamme instability of black strings in five space-time dimensions. We consider unstable black strings of fixed thickness and different lengths, and in all cases we confirm that at the intermediate stages of the evolution the horizon can be interpreted as a quasistationary self-similar sequence of black strings connecting spherical black holes on different scales. However, we do not find any evidence for a global timescale relating subsequent generations. The endpoint of the instability is the pinch off of the horizon in finite asymptotic time, thus confirming the violation of the weak cosmic censorship conjecture around black string spacetimes.