A class of dust-like self-similar solutions of the massless Einstein-Vlasov system

Abstract

In this paper the existence of a class of self-similar solutions of the Einstein-Vlasov system is proved. The initial data for these solutions are not smooth, with their particle density being supported in a submanifold of codimension one. They can be thought of as intermediate between smooth solutions of the Einstein-Vlasov system and dust. The motivation for studying them is to obtain insights into possible violation of weak cosmic censorship by solutions of the Einstein-Vlasov system. By assuming a suitable form of the unknowns it is shown that the existence question can be reduced to that of the existence of a certain type of solution of a four-dimensional system of ordinary differential equations depending on two parameters. This solution starts at a particular point $P_0$ and converges to a stationary solution $P_1$ as the independent variable tends to infinity. The existence proof is based on a shooting argument and involves relating the dynamics of solutions of the four-dimensional system to that of solutions of certain two- and three-dimensional systems obtained from it by limiting processes.

arXiv comment47 pages

References in corpus (5)

• Critical phenomena in gravitational collapse
• The Einstein-Vlasov system/Kinetic theory
• Critical collapse of collisionless matter - a numerical investigation
• Critical phenomena at the threshold of black hole formation for collisionless matter in spherical symmetry
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• Models for Self-Gravitating Photon Shells and Geons
• Examples of naked singularity formation in higher-dimensional Einstein-vacuum spacetimes
• Veiled singularities for the spherically symmetric massless Einstein-Vlasov system
• Spherical accretion of a collisionless kinetic gas into a generic static black hole
• The Einstein-Vlasov system in spherical symmetry II: spherical perturbations of static solutions