Fate of the Black String Instability

TL;DR

This paper argues that the classical horizon of unstable black strings cannot pinch off and instead stabilizes into new static solutions, challenging the common belief about black string fragmentation.

Contribution

It provides a theoretical argument showing that classical event horizons cannot pinch off, implying black strings evolve into non-uniform static solutions rather than breaking apart.

Findings

Classical horizons cannot pinch off under mild assumptions.

Unstable black strings settle into non-uniform static solutions.

Challenges the belief that black string instability leads to black hole formation.

Abstract

Gregory and Laflamme showed that certain nonextremal black strings (and p-branes) are unstable to linearized perturbations. It is widely believed that this instability will cause the black string horizon to classically pinch off and then quantum mechanically separate, resulting in higher dimensional black holes. We argue that this cannot happen. Under very mild assumptions, classical event horizons cannot pinch off. Instead, they settle down to new static black string solutions which are not translationally invariant along the string.