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

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-C961-3 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-C964-E
Genre: Journal Article

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1009.2596 (Preprint), 461KB
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 Creators:
Rendall, Alan D.1, Author              
Velazquez, Juan J. L., Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc
 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.

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 Dates: 2010-09-1420112011
 Publication Status: Published in print
 Pages: 47 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1009.2596
URI: http://arxiv.org/abs/1009.2596
DOI: 10.1007/s00023-011-0094-3
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Title: Annales Henri Poincare
Source Genre: Journal
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Publ. Info: Basel : Birkhäuser
Pages: - Volume / Issue: 12 (5) Sequence Number: - Start / End Page: 919 - 964 Identifier: ISSN: 1424-0637
CoNE: /journals/resource/954925494977_2