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

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##### Fulltext (public)

1009.2596

(Preprint), 461KB

AHP_12_05_919.pdf

(Any fulltext), 549KB

##### Supplementary Material (public)

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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.