论文标题
固定和轴向对称空间的曲率奇异性附近的大地测量学
Geodesics near a curvature singularity of stationary and axially symmetric space-times
论文作者
论文摘要
在这项工作中，我们研究了在固定和轴向对称的空间时间中包含的曲率奇异性附近地球化学的局部行为。除这些属性外，我们将重点介绍的指标也将被要求承认它们的大地测量学不可或缺的一部分。特别是，我们搜索了无效的时空几何形状的条件，而无效的大地测量学可以达到奇异性。这些条件取决于自由落体粒子的运动方程。我们还分析了在遇到路径中奇异性时并没有变得不完整的大地测量学的可能存在。结果将结果表示为依赖于逆度张量以及能量和角动量等保守量的标准。例如，派生的标准应用于Plebanski-Demianski的空间时间。最后，我们提出了一个线元素，该线元素描述了一个虫洞，其曲率奇异性根据我们的结果是因果土生来说无法访问的。
In this work we study the local behavior of geodesics in the neighborhood of a curvature singularity contained in stationary and axially symmetric space-times. Apart from these properties, the metrics we shall focus on will also be required to admit a quadratic first integral for their geodesics. In particular, we search for the conditions on the geometry of the space-time for which null and time-like geodesics can reach the singularity. These conditions are determined by the equations of motion of a freely-falling particle. We also analyze the possible existence of geodesics that do not become incomplete when encountering the singularity in their path. The results are stated as criteria that depend on the inverse metric tensor along with conserved quantities such as energy and angular momentum. As an example, the derived criteria are applied to the Plebanski-Demianski class of space-times. Lastly, we propose a line element that describes a wormhole whose curvature singularities are, according to our results, inaccessible to causal geodesics.
