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

Francisco Gonzalez Montoya

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arXiv · 2403.19846

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

Francisco Gonzalez Montoya

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Abstract

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.

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gr-qc math-ph math.MP nlin.CD

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BibTeX RIS

Francisco Gonzalez Montoya. 2024-03-28. Impenetrable Barriers in the Phase Space of a Particle Moving Around a Kerr Rotating Black Hole. https://arxiv.org/abs/2403.19846

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