On Shear-Free perturbations of FLRW Universes

Abstract

A surprising exact result for the Einstein Field Equations is that if pressure-free matter is moving in a shear-free way, then it must be either expansion-free or rotation-free. It has been suggested this result is also true for any barotropic perfect fluid, but a proof has remained elusive. We consider the case of barotropic perfect fluid solutions linearized about a Robertson-Walker geometry, and prove that the result remains true except for the case of a specific highly non-linear equation of state. We argue that this equation of state is non-physical, and hence the result is true in the linearized case for all physically realistic barotropic perfect fluids. This result, which is not true in Newtonian cosmology, demonstrates that the linearized solutions, believed to result in standard local Newtonian theory, do not always give the usual behaviour of Newtonian solutions.

References in corpus (2)

• Cosmic microwave background anisotropies: Nonlinear dynamics
• Covariant Analysis of Gravitational Waves in a Cosmological Context

Cited by in corpus (6)

• Backreaction in late-time cosmology
• Shear-free perfect fluids with linear equation of state
• Shear-free perfect fluids with a barotropic equation of state in general relativity: the present status
• Matter shear and vorticity in conformally flat spacetimes
• Shear-free conditions of a Chaplygin-Gas-dominated universe
• Reviving The Shear-Free Perfect Fluid Conjecture In General Relativity