Title: Phase space mixing in the vicinity of a Kerr black hole

Abstract:

Black holes are among the most spectacular predictions of Einstein's theory of general relativity (GR), and nowadays they constitute an active topic of research in astronomy, theoretical physics and mathematics. In this talk, I will start by providing a brief summary of the most important and intriguing properties of black holes (as solutions of Einstein's vacuum field equations). Next, some known facts regarding the geodesic motion in a Kerr spacetime (describing a rotating black hole in GR) and its formulation as an integrable Hamiltonian system will be reviewed. Finally, I will discuss the dynamical behavior of a collisionless kinetic gas propagating in the gravitational potential of a Kerr black hole, focusing on the regime where the individual gas particles move on bound orbits confined to the equatorial plane. It will be shown that even though collisions between gas particles are neglected, the gas undergoes a relaxation phenomena and converges in time to a stationary, axisymmetric configuration surrounding the black hole. This effect, like similar effects encountered in plasma physics and galactic dynamics, is due to the mixing property of the Hamiltonian phase flow, which implies that the one-particle distribution function converges weakly to a distribution function depending only on constants of motion.

This investigation was performed in collaboration with my former PhD student Paola Rioseco and is partially motivated by the need to thoroughly understand the behavior of matter in the vicinity of supermassive black holes in view of recent and ongoing observations at the Event Horizon Telescope.