非动力学Chern-Simons修正引力中Gödel型度规的一阶微扰
First-order perturbations of Gödel-type metrics in non-dynamical Chern-Simons modified gravity
摘要：
哥德尔型度规在空间和时间上都是齐次的，就像史瓦西度规一样，在陈-西蒙斯修正引力中保持一致;这在非动力学和动力学框架中都是如此，每一个框架都涉及一个耦合到庞特里亚金密度的额外赝标场。在本文中，我们考虑在非动力学框架中这些度量的平稳一阶扰动。在一定的假设下，我们找到了扰动场方程的解析解。一阶场方程的解打破了未扰动度规的平移对称性和圆柱对称性。控制平面测地线轨道的有效势也受到微扰参数的影响，它改变了有质量粒子和无质量光子轨道的平衡半径。
英文摘要：
Gödel-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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