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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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 Urheber:
Rendall, Alan D.1, Autor           
Velazquez, Juan J. L., Autor
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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Schlagwörter: General Relativity and Quantum Cosmology, gr-qc
 Zusammenfassung: 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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 Datum: 2010-09-1420112011
 Publikationsstatus: Erschienen
 Seiten: 47 pages
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Titel: Annales Henri Poincare
Genre der Quelle: Zeitschrift
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Ort, Verlag, Ausgabe: Basel : Birkhäuser
Seiten: - Band / Heft: 12 (5) Artikelnummer: - Start- / Endseite: 919 - 964 Identifikator: ISSN: 1424-0637
CoNE: https://pure.mpg.de/cone/journals/resource/954925494977_2