Plane symmetric analogue of NUT space

TL;DR

This paper introduces a new definition of spacetime symmetry based on curvature invariants and finds exact vacuum solutions of Einstein's equations that serve as plane symmetric analogues of NUT space, including static and stationary cases.

Contribution

It proposes a novel symmetry concept and derives a family of plane symmetric NUT-like solutions using (1+3)-decomposition formalism.

Findings

Found a two-parameter family of solutions with gravitomagnetic fields

Extended NUT space concept to plane symmetric spacetimes

Provided exact vacuum solutions for static and stationary cases

Abstract

In this article on the basis of a new definition of spacetime symmetry, which is in accordance with the symmetry of the curvature invariants, we investigate exact vacuum solutions of Einstein field equations corresponding to both static and stationary plane symmetric spacetimes using the concepts of the (1+3)-decomposition or threading formalism. Demanding the presence of a plane symmetric gravitomagnetic field we find a family of two parameter (m and l) solutions, every member of which being the plane symmetric analogue of NUT space.