Purely radiative perfect fluids with degenerate shear tensor

TL;DR

This paper investigates non-rotating geodesic perfect fluid spacetimes with purely radiative gravitational fields, showing that degeneracy in shear tensor leads to hypersurface homogeneous solutions of Bianchi class A.

Contribution

It demonstrates that in such spacetimes, a degenerate shear tensor implies commutation of H, E, and S, resulting in hypersurface homogeneous Bianchi class A solutions.

Findings

H, E, and S tensors commute when shear tensor is degenerate

Spacetimes are hypersurface homogeneous of Bianchi class A

Purely electric exceptions are identified

Abstract

We consider non-rotating geodesic perfect fluid spacetimes which are purely radiative in the sense that the gravitational field satisfies the covariant transverse conditions div H = div E = 0. We show that when the shear tensor S is degenerate, H, E and S necessarily commute and hence the resulting spacetimes are hypersurface homogeneous of Bianchi class A (modulo some purely electric exceptions).