黎曼和Sasaki时空中的暗引力场
Dark Gravitational Field on Riemannian and Sasaki Spacetime
摘要：
本文的目的是提供一个引力场的几何结构，其中包括添加暗物质的框架中的黎曼和Riemann-Sasaki时空。通过经典的黎曼几何方法，我们得到了修正的测地线方程，潮汐力，爱因斯坦和Raychaudhuri方程来解释额外的暗引力。我们进一步研究这种方法在宇宙学中的应用。此外，为了考察暗物质在具有更多自由度的引力统一几何模型中的行为，还研究了该模型在切丛上的可能扩展。将特别强调在暗物质影响下的测地线运动问题。
英文摘要：
The aim of this paper is to provide the geometrical structure of a gravitational field that includes the addition of dark matter in the framework of a Riemannian and a Riemann--Sasaki spacetime. By means of the classical Riemannian geometric methods we arrive at modified geodesic equations, tidal forces, and Einstein and Raychaudhuri equations to account for extra dark gravity. We further examine an application of this approach in cosmology. Moreover, a possible extension of this model on the tangent bundle is studied in order to examine the behavior of dark matter in a unified geometric model of gravity with more degrees of freedom. Particular emphasis shall be laid on the problem of the geodesic motion under the influence of dark matter.
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