Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 39, Issue 2, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1361-6382/ac3e50
Keywords
modified gravity; Godel-type metric; CPT symmetry breaking
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Funding
- Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) [301 562/2 019-9]
- Brazilian agency CAPES [88887.464556/2019-00]
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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.
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.
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