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Dynamics and stability of the Gödel universe

We use covariant techniques to describe the properties of the Gödel universe and then consider its linear response to a variety of perturbations. Against matter aggregations, we find that the stability of the Gödel 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 Gödel 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 Gödel model against linear gravity-wave distortions. The implications of the background rotation for scalar-field Gödel cosmologies are also discussed.