Help Guide Disclaimer Contact us Login
  Advanced SearchBrowse




Journal Article

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


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

There are no locators available
Fulltext (public)

(Preprint), 461KB

(Any fulltext), 549KB

Supplementary Material (public)
There is no public supplementary material available

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:
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.