Cylindrical analogue of NUT space: spacetime of a line gravomagnetic monopole

TL;DR

This paper derives a new cylindrically symmetric spacetime solution in general relativity representing a line gravomagnetic monopole, extending known solutions like Levi-Civita and NUT metrics.

Contribution

It introduces a novel vacuum solution for a line gravomagnetic monopole using the quasi-Maxwell form of Einstein equations, generalizing Levi-Civita and NUT metrics.

Findings

Derived the spacetime metric for a line gravomagnetic monopole.

Established the relation to Levi-Civita and NUT metrics.

Discussed features and connections to other solutions.

Abstract

Using the quasi-Maxwell form of the vacuum Einstein equations and demanding the presence of a cylindrically symmetric radial gravomagnetic field, we find the solution to the Einstein equations which represents the gravity field of a line gravomagnetic monopole. We show that this is the generalization of the Levi-Civita's cylindrically symmetric static spacetime, in the same way that the NUT metric is the empty space generalization of the Schwarzschild metric. Some of the features of this metric as well as its relation to other metrics are discussed.