First-order perturbations of Godel-type metrics in non-dynamical Chern-Simons modified gravity

Godel-type metrics that are homogeneous in both space and time remain, like the Schwarzschild metric, consistent within Chern-Simons modified gravity; this is true in both the non-dynamical and dynamical frameworks, each of which involves an additional pseudoscalar field coupled to the Pontryagin density. In this paper, we consider stationary first-order perturbations to these metrics in the non-dynamical framework. Under certain assumptions we find analytical solutions to the perturbed field equations. The solutions of the first-order field equations break the translational and cylindrical symmetries of the unperturbed metrics. The effective potential controlling planar geodesic orbits is also affected by the perturbation parameter, which changes the equilibrium radii for the orbits of both massive particles and massless photons.

Automated summary

This paper investigates the first-order perturbations of Godel-type metrics in the non-dynamical framework. By solving the perturbed field equations, it is found that the first-order field equations break the symmetries of the unperturbed metrics and affect the equilibrium radii of planar geodesic orbits.