A spherically symmetric dust-space-time with a NUT-like rotation

TL;DR

This paper derives a new solution to Einstein's equations describing a dust-filled, spherically symmetric spacetime with NUT-like rotation, featuring closed timelike geodesics and a Minkowski limit.

Contribution

It introduces a novel exact solution of Einstein's equations using Mitskievich's field theory, combining spherical symmetry with NUT-like rotation.

Findings

Solution is Petrov type D.

Admits closed timelike geodesics.

Reduces to Minkowski space when dust and rotation vanish.

Abstract

A deduction of a solution of the Einstein's equations, employing the Mitskievich's field theoretic description of perfect fluids, is presented. This solution describes a dust-space-time with a spherical-like symmetry and a NUT-like rotation. This solution is of Petrov type D, and has an isometry group G4. It also admits closed timelike geodesics. It has Minkowski space-time as a limit, when both dust and rotation disappear.