# Francisco González Montoya: Impenetrable Barriers in the Phase Space of a Particle Moving Around a Rotating Black Hole

Date of publication: 27. 8. 2024

Mathematical physics seminar

Thursday

12

September

Time:

14:00 - 16:00

Location:

Seminar room 133 (Jadranska Ulica 21)

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 Manifolds, and their 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.