Abstract
Due to the complexity of the axially symmetric Einstein-Vlasov system there are no analytic results available in the literature for evolution problems except in the case of small initial data. By using numerical methods it is however possible to gain insights for general initial data. In this talk I will briefly discuss the particle in cell (PIC) method that is often used to treat Vlasov matter numerically and I will present results from two recent studies that I have carried out together with Ellery Ames and Oliver Rinne. We study gravitational collapse, in particular critical collapse, and it will be seen that a quantity that strongly affects the faith of a solution is the binding energy. We also study the Hoop conjecture and the weak cosmic censorship conjecture (WCCC). We seriously test the WCCC in two cases. In the first case we launch initial data for which the total angular momentum J satisfy |J|>M^2 which in view of the Kerr solution is a threat to the WCCC. In the second case we launch highly prolate initial data which in view of the Hoop conjecture also is a threat to the WCCC. It is remarkable how the matter configuration changes shape and properties in the evolution in order not to violate the WCCC which holds in all cases we study. I will also discuss some open problems.
Speaker Intro
My research is in general relativity and I am interested in questions about spacetime singularities and cosmic censorship. The cosmic censorship conjecture was proposed by Roger Penrose in the sixties and the hypothesis is that spacetime singularities are always hidden within black holes and cannot be seen (i.e. there are no "naked singularities"). In my research I primarily work on global existence for solutions to Einstein's equations and in particular to the Einstein-Vlasov system where the matter is modelled by kinetic theory. A global existence theorem is the first step towards an understanding of cosmic censorship. I am also interested in kinetic equations in general (on a flat background spacetime) such as the Maxwell-Vlasov system, the Vlasov-Poisson system and the relativistic Boltzmann equation.
