标题： 粒子在克尔旋转黑洞相空间中的不可穿透屏障 显示英文标题

标题： Impenetrable Barriers in the Phase Space of a Particle Moving Around a Kerr Rotating Black Hole

摘要： 我们从几何角度研究了在由Kerr度规描述的旋转黑洞引力场中运动粒子的相空间。 特别是，我们展示了不稳定的周期轨道的多维推广的构造，称为正常双曲不变流形，以及引导相空间中动力学的稳定和不稳定不变流形。 这些稳定和不稳定不变流形分割了相空间，并且在扰动下具有鲁棒性。 为了可视化相空间中流动下的多维不变集，我们使用了一种基于相空间中轨迹弧长的方法，该方法在文献中被称为拉格朗日描述符。 显示英文摘要

摘要： We study the phase space of a particle moving in the gravitational field of a rotating black hole described by the Kerr metric from a geometrical perspective. In particular, we show the construction of a multidimensional generalization of the unstable periodic orbits, known as Normally Hyperbolic Invariant Manifold, and its stable and unstable invariant manifolds that direct the dynamics in the phase space. Those stable and unstable invariant manifolds divide the phase space and are robust under perturbations. To visualize the multidimensional invariant sets under the flow in the phase space, we use a method based on the arclength of the trajectories in phase space known as Lagrangian descriptors in the literature.