Dynamics and stability of the Godel universe

TL;DR

This paper investigates the stability and response of the Godel universe to various perturbations, revealing conditions under which it remains stable or becomes unstable, with implications for rotating cosmological models.

Contribution

It provides a detailed linear perturbation analysis of the Godel universe using covariant techniques, highlighting stability conditions related to matter gradients and fluid equations of state.

Findings

Stability depends on gradients in centrifugal energy.

Magnetic Weyl component obeys a plane-wave equation, indicating neutral stability.

Vorticity evolves similarly to almost-FRW spacetimes with directional effects.

Abstract

We use covariant techniques to describe the properties of the Godel universe and then consider its linear response to a variety of perturbations. Against matter aggregations, we find that the stability of the Godel model depends primarily upon the presence of gradients in the centrifugal energy, and secondarily on the equation of state of the fluid. The latter dictates the behaviour of the model when dealing with homogeneous perturbations. The vorticity of the perturbed Godel model is found to evolve as in almost-FRW spacetimes, with some additional directional effects due to shape distortions. We also consider gravitational-wave perturbations by investigating the evolution of the magnetic Weyl component. This tensor obeys a simple plane-wave equation, which argues for the neutral stability of the Godel model against linear gravity-wave distortions. The implications of the background rotation for scalar-field Godel cosmologies are also discussed.