Rotating and twisting locally rotationally symmetric spacetimes: a general solution

TL;DR

This paper derives a comprehensive solution for the most general rotating and twisting locally rotationally symmetric spacetimes, revealing their self-similar nature and potential cosmological and astrophysical implications.

Contribution

It introduces a novel general solution for rotating and twisting LRS spacetimes using a 1+1+2 formalism and self-similarity, expanding understanding of their structure.

Findings

Spacetime class must be self-similar

Derived a general solution for these spacetimes

Discussed cosmological and astrophysical implications

Abstract

In this paper we derive a general solution for the most general rotating and twisting locally rotationally symmetric spacetimes. This is achieved in three steps. First we decompose the manifold via 1+1+2 semi-tetrad formalism that yields a set of geometrical and thermodynamic scalars for the spacetime. We then recast the Einstein field equations in terms of evolution and propagation of these scalars. It is then shown that this class of spacetimes must possess self similarity and we use this property to solve for these scalars, thus obtaining a general solution. This solution has a number of very interesting cosmological or astrophysical consequences which we discuss in detail.