This project consists in modeling the dynamics of a set of collisionless particles that describe a source of matter (such as an ensemble of stars, or a dilute gas) in a strong gravity regime. This scenario is described by the Vlasov equation coupled with Einstein equations (Namely, Einstein - Vlasov system). The goal is to investigate the dynamics of a self-gravitating accretion disk around a spinning black hole (like a supermassive black hole present at the galaxy center).
I worked during my Phd Thesis on a similar problem where I neglected the self gravity of the disk. I approximated it as a thin disk (two dimensional model). The main result of this work was a very interesting one, in which any initial disk configuration relaxes to an axisymmetric and stationary configuration that is determined only by conserved quantities, not by any dissipation mechanism but simply by the so-called "phase-space mixing.
In this project I will investigate if phase space mixing still works when self-gravity is taken into account. Some of the critical questions I try to answer are 1) if when one takes gravity into account (perturbatively, in the case of the project) will there be chaos in the neighbourhood of resonant orbits? 2) Can chaos be suppressed by the phase space mixing?