On cosmic censorship for the Einstein-Vlasov system: A numerical study of the spherically symmetric Einstein-Vlasov system for dust-like initial data

Abstract

Already in the first solution of the Einstein field equations of general relativity, singularities appeared. A great deal of effort has since been put into understanding these objects. If there exist singularities from which matter or light could escape, it would lead to a breakdown of the predictability of the Einstein field equations. The concept of cosmic censorship, which asserts that no such singularities exist, is thus fundamental to the theory of general relativity and has been debated in the community ever since it was first conjectured. In this thesis, cosmic censorship is investigated numerically in the spherically symmetric, asymptotically flat Einstein- Vlasov system. The Vlasov matter model is compared to the more primitive dust model, which is known to generate naked singularities that contradict cosmic censorship. The Einstein-Vlasov system is simulated with a Particle In Cell method. The results indicate that initial data that is known to produce naked singularities in dust matter does not give naked singularities in Vlasov matter with large initial velocity dispersion. Moreover, it is shown that the Einstein-Vlasov system can approximate the dust system arbitrarily well up to numerical accuracy. In order to show that cosmic censorship holds even for Vlasov matter that is initially arbitrarily close to dust, better precision in the simulations and a combination of numerical and analytical studies are needed.