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

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons20696

Rendall,  Alan D.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1009.2596
(Preprint), 461KB

AHP_12_05_919.pdf
(Any fulltext), 549KB

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Citation

Rendall, A. D., & Velazquez, J. J. L. (2011). A class of dust-like self-similar solutions of the massless Einstein-Vlasov system. Annales Henri Poincare, 12(5), 919-964. doi:10.1007/s00023-011-0094-3.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-C961-3
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.