Evidence that highly non-uniform black strings have a conical waist

TL;DR

This paper provides numerical evidence supporting the conjecture that highly non-uniform black strings develop a conical waist, and extends this idea to weakly charged strings, enhancing understanding of their geometric structure.

Contribution

The authors explicitly test and support the conjecture that the waist of highly non-uniform black strings is conical, and extend the analysis to include weakly charged strings.

Findings

Strong numerical evidence for conical waist in highly non-uniform black strings

Extension of the conical waist conjecture to weakly charged strings

Insights into the local geometry of non-uniform black strings

Abstract

Numerical methods have allowed the construction of vacuum non-uniform strings. For sufficient non-uniformity, the local geometry about the minimal horizon sphere (the "waist") was conjectured to be a cone metric. We are able to test this conjecture explicitly giving strong evidence in favour of it. We also show how to extend the conjecture to weakly charged strings.