Maximally inhomogeneous G\"{o}del-Farnsworth-Kerr generalizations

TL;DR

This paper explores inhomogeneous generalizations of known G"odel-Farnsworth-Kerr solutions, analyzing their geometric properties and constructing their line elements, thus extending the understanding of rotating perfect fluid space-times.

Contribution

It introduces new inhomogeneous solutions with non-constant rotation, expanding the class of known G"odel-Farnsworth-Kerr type space-times.

Findings

Identified inhomogeneous solutions with non-constant rotation

Constructed explicit line elements for these solutions

Analyzed local geometric properties of the new solutions

Abstract

It is pointed out that physically meaningful aligned Petrov type D perfect fluid space-times with constant zero-order Riemann invariants are either the homogeneous solutions found by G\"{o}del (isotropic case) and Farnsworth and Kerr (anisotropic case), or new inhomogeneous generalizations of these with non-constant rotation. The construction of the line element and the local geometric properties for the latter are presented.