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Dark energy and extending the geodesic equations of motion: A spectrum of galactic rotation curves
General Relativity and Gravitation ( IF 2.8 ) Pub Date : 2022-07-20 , DOI: 10.1007/s10714-022-02949-w
Achilles D. Speliotopoulos

A recently proposed extension of the geodesic equations of motion, where the worldline traced by a test particle now depends on the scalar curvature, is used to study the formation of galaxies and galactic rotation curves. This extension is applied to the motion of a fluid in a spherical geometry, resulting in a set of evolution equations for the fluid in the nonrelativistic and weak gravity limits. Focusing on the stationary solutions of these equations and choosing a specific class of angular momenta for the fluid in this limit, we show that dynamics under this extension can result in the formation of galaxies with rotational velocity curves (RVC) that are consistent with the Universal Rotation Curve (URC), and through previous work on the URC, the observed rotational velocity profiles of 1100 spiral galaxies. In particular, a spectrum of RVCs can form under this extension, and we find that the two extreme velocity curves predicted by it brackets the ensemble of URCs constructed from these 1100 velocity profiles. We also find that the asymptotic behavior of the URC is consistent with that of the most probable asymptotic behavior of the RVCs predicted by the extension. A stability analysis of these stationary solutions is also done, and we find them to be stable in the galactic disk, while in the galactic hub they are stable if the period of oscillations of perturbations is longer than \(0.91_{\pm 0.31}\) to \(1.58_{\pm 0.46}\) billion years.



中文翻译:

暗能量和运动测地线方程的扩展:银河自转曲线谱

最近提出的测地线运动方程的扩展,其中测试粒子追踪的世界线现在取决于标量曲率,用于研究星系的形成和星系旋转曲线。该扩展应用于球形几何中的流体运动,从而产生一组非相对论和弱重力限制中的流体演化方程。着眼于这些方程的静止解,并为该极限内的流体选择特定类别的角动量,我们表明在此扩展下的动力学可以导致形成具有与通用的旋转速度曲线(RVC)一致的星系旋转曲线 (URC),并通过之前对 URC 的工作,观察到 1100 个螺旋星系的旋转速度分布。尤其是,在此扩展下可以形成一系列 RVC,我们发现它预测的两条极端速度曲线包含了由这 1100 个速度剖面构建的 URC 集合。我们还发现 URC 的渐近行为与扩展预测的 RVC 的最可能渐近行为一致。还对这些静止解进行了稳定性分析,我们发现它们在银盘中是稳定的,而在星系中心,如果扰动的振荡周期长于 我们还发现 URC 的渐近行为与扩展预测的 RVC 的最可能渐近行为一致。还对这些静止解进行了稳定性分析,我们发现它们在银盘中是稳定的,而在星系中心,如果扰动的振荡周期长于 我们还发现 URC 的渐近行为与扩展预测的 RVC 的最可能渐近行为一致。还对这些静止解进行了稳定性分析,我们发现它们在银盘中是稳定的,而在星系中心,如果扰动的振荡周期长于\(0.91_{\pm 0.31}\)\(1.58_{\pm 0.46}\)十亿年。

更新日期:2022-07-21
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