Black Rings, Boosted Strings and Gregory-Laflamme

TL;DR

This paper studies the Gregory-Laflamme instability in boosted black strings with KK-momentum, revealing how internal velocity affects the instability threshold and suggesting the existence of black rings in various dimensions.

Contribution

It establishes a relation between instability thresholds for boosted and static black strings and proposes the existence of black rings in arbitrary dimensions based on these results.

Findings

Threshold of classical instability depends on boost velocity.

Sorkin's critical dimension varies with internal velocity and can vanish.

Black rings are likely to exist in any number of space-time dimensions.

Abstract

We investigate the Gregory-Laflamme instability for black strings carrying KK-momentum along the internal direction. We demonstrate a simple kinematical relation between the thresholds of the classical instability for the boosted and static black strings. We also find that Sorkin's critical dimension depends on the internal velocity and in fact disappears for sufficiently large boosts. Our analysis implies the existence of an analogous instability for the five-dimensional black ring of Emparan and Reall. We also use our results for boosted black strings to construct a simple model of the black ring and argue that such rings exist in any number of space-time dimensions.