Shear-Free Gravitational Waves in an Anisotropic Universe

TL;DR

This paper investigates shear-free gravitational waves in an anisotropic Bianchi I universe, showing that pure gravitational radiation occurs only on shear-free null hypersurfaces and providing explicit gauge-invariant perturbations.

Contribution

It demonstrates the conditions for shear-free gravitational waves in anisotropic universes and explicitly computes gauge-invariant perturbations, extending understanding beyond isotropic models.

Findings

Pure gravitational radiation requires shear-free null hypersurfaces.

Explicit gauge-invariant perturbations are derived.

Differences from isotropic cases are clearly shown.

Abstract

We study gravitational waves propagating through an anisotropic Bianchi I dust-filled universe (containing the Einstein-de-Sitter universe as a special case). The waves are modeled as small perturbations of this background cosmological model and we choose a family of null hypersurfaces in this space-time to act as the histories of the wavefronts of the radiation. We find that the perturbations we generate can describe pure gravitational radiation if and only if the null hypersurfaces are shear-free. We calculate the gauge-invariant small perturbations explicitly in this case. How these differ from the corresponding perturbations when the background space-time is isotropic is clearly exhibited.