论文标题
在$ \ textrm {sads} _4 $ spaceTime中的地球一致性和Raychaudhuri方程式
On Geodesic Congruences and the Raychaudhuri Equations in $\textrm{SAdS}_4$ Spacetime
论文作者
论文摘要
在本文中，我们研究了（3+1）时空维度的Schwarzschild-anti-de保姆度量。我们研究了边缘结合的大地测量学类别（时机和空），同时将其行为与正常的Schwarzschild指标进行了比较。使用$ \ textIt {Mathematica} $，我们在此指标中计算了剪切和旋转张量，以及Raychaudhuri方程的其他组件，我们认为在赤道飞机上略有界限的时间表地测量，始终有一个转折点，而它们的null类似物至少有一个不属于地球的家族。我们还提出了赤道平面中的大地测量和地球一致性的相关图。
In this article, we look into geodesics in the Schwarzschild-Anti-de Sitter metric in (3+1) spacetime dimensions. We investigate the class of marginally bound geodesics (timelike and null), while comparing their behavior with the normal Schwarzschild metric. Using $\textit{Mathematica}$, we calculate the shear and rotation tensors, along with other components of the Raychaudhuri equation in this metric and we argue that marginally bound timelike geodesics, in the equatorial plane, always have a turning point, while their null analogues have at least one family of geodesics that are unbound. We also present associated plots for the geodesics and geodesic congruences, in the equatorial plane.
