Abstract

The equations of motion of a test particle are integrated for the field of a rotating Kerr black hole (BH) (in accordance with [1]). Due to the lack of analytical transformations for the Carter–Penrose diagrams (CPDs) for the Kerr metric, the topology of the Kerr BH is studied by analytical investigation of the equations of motion. Transformations for the CPDs for the Reisner–Nordström metric are analyzed. The problem of boundary conditions for the Reisner–Nordström topology is analyzed. A solution to this problem of boundary conditions is proposed. It is proved that, in the Reisner–Nordström topology, only one way to go to another universe is possible. For the Kerr topology, the possibility of the existence of an alternative transition to another universe that does not coincide with the universe for the ordinary transition is found. This alternative transition is performed through a surface with a zero radial coordinate (zero radius). Initial conditions for the falling particle are found that correspond to an alternative transition to another universe. The tidal forces acting on a falling body in the Kerr metric are estimated, and the possibility of the transition of the body to other universes without being destroyed by tidal forces is proved.

中文翻译：

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Kerr度量的拓扑分析

摘要

对于旋转的Kerr黑洞（BH）的场，对测试粒子的运动方程进行了积分（根据[1]）。由于缺少Kerr度量的Carter-Penrose图（CPD）的解析变换，因此通过对运动方程的解析研究来研究Kerr BH的拓扑。分析了Reisner–Nordström指标的CPD转换。分析了Reisner–Nordström拓扑的边界条件问题。提出了对边界条件问题的解决方案。事实证明，在Reisner–Nordström拓扑中，只有一种方法可以进入另一个宇宙。对于Kerr拓扑，发现存在与普通过渡不同的另一过渡过渡的可能性。通过具有零径向坐标（零半径）的曲面执行此替代过渡。发现下降粒子的初始条件对应于向另一个宇宙的替代过渡。估算了以克尔度量的作用在坠落物体上的潮汐力，并证明了该物体在不被潮汐力破坏的情况下过渡到其他宇宙的可能性。