Stable non-uniform black strings below the critical dimension

TL;DR

This paper constructs and analyzes non-uniform black string solutions in various dimensions, revealing stability properties that challenge previous expectations, especially in 12 and 13 dimensions.

Contribution

It provides numerical solutions for non-uniform black strings in 11-15 dimensions and investigates their stability, showing stability in higher dimensions and unexpected stability in some lower dimensions.

Findings

Strongly non-uniform solutions in 12 and 13 dimensions are stable.

All non-uniform black strings in 14 and 15 dimensions are stable.

Weakly non-uniform solutions behave as expected.

Abstract

The higher-dimensional vacuum Einstein equation admits translationally non-uniform black string solutions. It has been argued that infinitesimally non-uniform black strings should be unstable in 13 or fewer dimensions and otherwise stable. We construct numerically non-uniform black string solutions in 11, 12, 13, 14 and 15 dimensions. Their stability is investigated using local Penrose inequalities. Weakly non-uniform solutions behave as expected. However, in 12 and 13 dimensions, strongly non-uniform solutions appear to be stable and can have greater horizon area than a uniform string of the same mass. In 14 and 15 dimensions all non-uniform black strings appear to be stable.