Stationary vacuum hyper-cylindrical solution in 4+1 dimensions

TL;DR

This paper presents a new 4+1 dimensional stationary vacuum hyper-cylindrical solution characterized by mass, tension, and momentum, expanding understanding of higher-dimensional gravitational solutions.

Contribution

It introduces a novel stationary hyper-cylindrical solution in 4+1 dimensions with specific physical parameters, extending static solutions to include momentum.

Findings

Solution characterized by mass, tension, and momentum

Locally equivalent to known static solutions

Brief discussion of physical properties

Abstract

We find a 4+1 dimensional stationary vacuum hyper-cylindrical solution solution which is spherically symmetric in $3-$dimensions and invariant under the translation along the fifth coordinate. The solution is characterized by three parameters, mass, tension, and conserved momentum along the fifth coordinate. The metric is locally equivalent to the known static solution. We briefly discuss its physical properties.