Fatima-Ezzahra Jabiri

The center of most galaxies can be described by a black hole with matter orbiting around it. In the context of relativistic kinetic theory, the Vlasov matter model is used to describe the center of galaxies, where the stars play the role of gas particles and collisions among them are neglected so that gravity is the only interaction taken into account. In this setting, stars are assumed to move along timelike future directed geodesics in a given spacetime.
In this talk,  we shall  are interested in the final states of  such self-gravitationg systems. These can be described by stationary  black hole solutions to the so-called Einstein-Vlasov system. One can construct them via a perturbation argument that relies on the  study of timelike geodesics  in black hole spacetimes that are close to a reference black hole solution (Schwarzschild or Kerr).  This approach will be detailed in this presentation.