Dynamics and stability of the Gödel universe

Abstract

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 gravitationalwave 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.

Yukawa-like confinement potential of a scalar particle in a Gödel-type spacetime with any l

“…Beside, Reboucas et al instituted three classes of solutions that are explained by the properties as: (a) solutions where there are no CTCs; (b) solutions with a sequence of alternating causal regions and not causal regions; (c) solutions explained by only one non-causal region [30,31]. In 2004 and 2005, Barrow et al analyzed the other properties such as the stability and dynamic of the Gödel model [32,33]. Summary, some of the authors have investigated the application of the Gödel space-time in matter.…”

Dynamics of the universe with global rotation

“…In the general relativistic case rotation is governed by a pair of nonlinear propagation and constraint equations which for the case of the barotropic equation of state reduces to [19] …”

“…Therefore, it is very difficult to consider both effects of anisotropy and rotation, that's why we study the Newtonian counterpart of model with rotation. Moreover, it is reasonable to assume that the shear scalar is sufficiently small compared with angular velocity scalar since the shear falls off more rapidly than the rotation as the universe expands [5,17,18,19].…”

The lightcone of Gödel-like spacetimes

“…The lightcone geometry of the Gödel family with 1 < k 2 < ∞ (k 2 = 2 corresponds to the Gödel cosmos [23], [24], [26], [5], [34], [35]) is studied in section 3, based on a paper by Calvão, Soares and Tiomno [10]. Further sections consider briefly some limiting cases.…”