Purely radiative perfect fluids

TL;DR

This paper characterizes a class of purely radiative, geodesic perfect fluids in cosmology, showing they are uniquely identified by the simultaneous diagonalizability of Weyl tensor parts and shear, with specific conditions on pressure and rotation.

Contribution

It provides a unique characterization of Bianchi class A perfect fluids with purely radiative conditions, extending previous classifications to include non-constant pressure and irrotational cases.

Findings

Bianchi class A perfect fluids are characterized by diagonalizable Weyl tensor parts and shear.

The characterization holds for non-constant pressure fluids and irrotational constant pressure fluids.

Purely electric and spherically symmetric universes are related classes within this characterization.

Abstract

We study `purely radiative' (div E = div H = 0) and geodesic perfect fluids with non-constant pressure and show that the Bianchi class A perfect fluids can be uniquely characterized --modulo the class of purely electric and (pseudo-)spherically symmetric universes-- as those models for which the magnetic and electric part of the Weyl tensor and the shear are simultaneously diagonalizable. For the case of constant pressure the same conclusion holds provided one also assumes that the fluid is irrotational.