Extraordinary vacuum black string solutions

TL;DR

This paper explores various stationary vacuum black string solutions in five dimensions, revealing that their spectrum includes black strings and wormholes, and clarifying the conditions under which these solutions exist.

Contribution

It identifies and analyzes a class of stationary vacuum solutions in 5D, showing the existence of black strings and wormholes beyond previously known naked singularities.

Findings

Solution spectrum includes black strings and wormholes

No new zero momentum solutions found

Solutions depend on momentum flow to mass ratio

Abstract

In addition to the boosted static solution there are two other classes of stationary string-like solutions of the vacuum Einstein equation in (4+1)-dimensions. Each class is characterized by three parameters of mass, tension, and momentum flow along the fifth coordinate. We analyze the metric properties of one of the two classes, which was previously assumed to be naked singular, and show that the solution spectrum contains black string and wormhole in addition to the known naked singularity as the momentum flow to mass ratio increases. Interestingly, there does not exist new zero momentum solution in these cases.