### Speaker: **Renato Velozo**

### Sorbonne Université, France

### Date: Monday, April 10, 2023 at 12 Santiago time

**Abstract: **I will present upcoming linear and non-linear stability results concerning the asymptotic behavior of collisionless many-particle systems on black hole exteriors. On the one hand, I will discuss decay properties for solutions to the massive Vlasov equation on Schwarzschild spacetime. On the other hand, I will discuss an asymptotic stability result for the exterior of Schwarzschild as a solution to the Einstein–massless Vlasov system, assuming spherical symmetry. I will explain the use of hyperbolic dynamics to obtain decay in time of the energy momentum tensor by considering a Vlasov equation with a trapping potential.

**Venue:** Online via Zoom / Sala seminarios DIM, 5th floor, Beauchef 851

**Chair:** Rayssa Caju