论文标题
riemannian流形到静态的静态
Riemannian manifolds dual to static spacetimes
论文作者
论文摘要
正如L. C. Epstein所建议的那样，我们在静态间距和Riemannian歧管之间建立了一对一的对应关系，该歧管将因果地球化学映射到地球学。然后，我们探索恒定的曲率空间 - 例如De Sitter和Anti -De Sitter Univers，并发现它们映射到恒定的曲率Riemannian歧管，即欧几里得空间，球体和双曲线空间。通过施加映射到球体所需的条件，我们获得了球形对称的指标，其中有径向振荡运动，其周期与振幅无关。然后，我们考虑完美的流体和爱因斯坦簇的情况，并确定找到这种运动所需的压力和密度曲线。最后，我们给出了与不表现出恒定曲率的某些类型运动相对应的表面的示例，例如Schwarzschild，Schwarzschild de Sitter和Schwarzschild抗DE固有解决方案，甚至用于简化的蠕虫模型。
We establish a one-to-one correspondence between static spacetimes and Riemannian manifolds that maps causal geodesics to geodesics, as suggested by L. C. Epstein. We then explore constant curvature spacetimes - such as the de Sitter and the anti-de Sitter universes - and find that they map to constant curvature Riemannian manifolds, namely the Euclidean space, the sphere and the hyperbolic space. By imposing the conditions required to map to the sphere, we obtain the spherically symmetric metrics for which there is radial oscillatory motion with a period independent of the amplitude. We then consider the case of a perfect fluid and an Einstein cluster and determine the pressure and density profiles required to find this type of motion. Finally, we give examples of surfaces corresponding to certain types of motion for metrics that do not exhibit constant curvature, such as the Schwarzschild, Schwarzschild de Sitter and Schwarzschild anti-de Sitter solutions, and even for a simplified model of a wormhole.
