Static Axisymmetric Vacuum Solutions and Non-Uniform Black Strings

TL;DR

This paper introduces new numerical methods for solving static axisymmetric vacuum Einstein equations in higher dimensions, focusing on non-uniform black strings and their properties near the Gregory-Laflamme critical point.

Contribution

It presents novel numerical techniques to analyze non-uniform black strings in higher dimensions and explores their physical properties and stability characteristics.

Findings

Computed solutions with horizon radius ratios up to nine.

Found that non-uniform black strings have larger mass than uniform strings at the same compactification radius.

Demonstrated these solutions are not the end state of the Gregory-Laflamme instability.

Abstract

We describe new numerical methods to solve the static axisymmetric vacuum Einstein equations in more than four dimensions. As an illustration, we study the compactified non-uniform black string phase connected to the uniform strings at the Gregory-Laflamme critical point. We compute solutions with a ratio of maximum to minimum horizon radius up to nine. For a fixed compactification radius, the mass of these solutions is larger than the mass of the classically unstable uniform strings. Thus they cannot be the end state of the instability.