## Journée thématique "Evolution equations in General Relativity". [1]

10h Håkan Andréasson (Chalmers University, Stockholm) : On the existence and structure of stationary solutions of the Einstein-Vlasov system.

Abstract: The present status on the existence and structure of static and stationary solutions of the Einstein-Vlasov system is reviewed. The structure of spherically symmetric static solutions is quite well understood. I will discuss a number of their features, in particular the case of charged solutions since they indicate what properties can be expected of axisymmetric stationary solutions. Existence of axially symmetric stationary solutions that are perturbed off from spherically symmetric Newtonian solutions have been obtained analytically whereas solutions far from being spherically symmetric have only been constructed numerically. I will discuss the properties of the latter. In particular, two different sequences of toroidal solutions which contain ergoregions will be described in detail. These solutions either approach an extreme Kerr black hole or they have the property that the geometry becomes conical in the limit and such solutions may provide models of cosmic strings.

11h Grigorios Fournodavlos (Sorbonne Université) : Linearised stability of relativistic ``hard stars''.

Abstract: We will study the dynamics of a 1-parameter family of static solutions to the spherically symmetric Einstein-Euler equations. These are described by a perfect fluid with a linear equation of state, modeling the hard core of a star that has undergone a supernova, but has not collapsed to a black hole. The first variational study of such stars, in general relativity, dates back to Harrison-Thorne-Wakano-Wheeler (1965). I will present recent work with Volker Schlue, where we treated the linearised Einstein-Euler equations, about these static solutions, in spherical symmetry. In particular, we will discuss two main features of the linearised dynamics of small hard stars, global-in-time boundedness of energy and the presence of periodic solutions to the linearised system of equations. We will then relate these properties to the orbital stability problem.

14h Lars Andersson (Einstein Institut, Golm) : Conservation laws for spinning fields.

15h Nicolas Besset (Université Grenoble Alpes) : The charged Klein-Gordon equation on the De Sitter-Reissner-Nordström metric.