Partially locally rotationally symmetric perfect fluid cosmologies

TL;DR

This paper proves that under certain symmetry assumptions, no new perfect fluid cosmological solutions exist beyond known classes, and it clarifies the conditions under which local rotational symmetry arises.

Contribution

It shows the non-existence of new solutions under specified symmetry conditions and refines the understanding of when local rotational symmetry is guaranteed in perfect fluid cosmologies.

Findings

No new solutions beyond known classes under the symmetry assumptions.

Local rotational symmetry follows from second-order covariant derivatives of the Riemann tensor.

Strengthens previous results on symmetry conditions in cosmological models.

Abstract

We show that there are no new consistent cosmological perfect fluid solutions when in an open neighbourhood ${\cal U}$ of an event the fluid kinematical variables and the electric and magnetic Weyl curvature are all assumed rotationally symmetric about a common spatial axis, specialising the Weyl curvature tensor to algebraic Petrov type D. The consistent solutions of this kind are either locally rotationally symmetric, or are subcases of the Szekeres dust models. Parts of our results require the assumption of a barotropic equation of state. Additionally we demonstrate that local rotational symmetry of perfect fluid cosmologies follows from rotational symmetry of the Riemann curvature tensor and of its covariant derivatives only up to second order, thus strengthening a previous result.