Matter shear and vorticity in conformally flat spacetimes

TL;DR

This paper investigates the behavior of matter shear and vorticity in conformally flat FLRW spacetimes, revealing their wave-like properties and their role in conveying curvature information without free gravitational waves.

Contribution

It provides a covariant, gauge-invariant analysis of matter shear and vorticity, showing they obey wave equations and influence spacetime curvature in linearized conformally flat cosmologies.

Findings

Matter shear satisfies a transverse traceless tensor wave equation.

Vorticity obeys a vector wave equation.

Shear and vorticity waves carry curvature information in the absence of gravitational waves.

Abstract

In this paper we consider conformally flat perturbations on the Friedmann Lemaitre Robertson Walker (FLRW) spacetime containing a general matter field. Working with the linearised field equations, we unearth some important geometrical properties of matter shear and vorticity and how they interact with the thermodynamical quantities in the absence of any free gravity powered by the Weyl curvature. As there are hardly any physically realistic rotating exact conformally flat solutions in general relativity, these covariant and gauge invariant results bring out transparently the role of vorticity in the linearised regime. Most interestingly, we demonstrate that the matter shear obeys a transverse traceless tensor wave equation, and the vorticity obeys a vector wave equation in this regime. These shear and vorticity waves replace the gravitational waves in the sense that they causally carry the information about local change in the curvature of these spacetimes.