First-order perturbations of G\"{o}del-type metrics in non-dynamical Chern-Simons modified gravity

TL;DR

This paper investigates first-order perturbations of G"odel-type metrics within non-dynamical Chern-Simons gravity, revealing symmetry breaking and modifications to geodesic orbits, thus advancing understanding of gravitational effects in this modified theory.

Contribution

It provides analytical solutions for first-order perturbations of G"odel-type metrics in non-dynamical Chern-Simons gravity, showing symmetry breaking and impact on geodesic stability.

Findings

Perturbed metrics break original symmetries.

Effective potential for geodesics is altered.

Equilibrium radii for particle and photon orbits change.

Abstract

G\"{o}del-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.