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  An introduction to the Einstein-Vlasov system

Rendall, A. D. (1997). An introduction to the Einstein-Vlasov system. In P. T. Chrusciel (Ed.), Mathematics of Gravitation: Part I: Lorentzian Geometry and Einstein Equatations (pp. 35-68). Warszawa: Polish Academy of Sciences, Institute of Mathematics.

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331296.pdf (Preprint), 305KB
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 Creators:
Rendall, Alan D.1, Author           
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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 Abstract: These lectures are designed to provide a general introduction to the Einstein-Vlasov system and to the global Cauchy problem for these equations. To start with some general facts are collected and a local existence theorem for the Cauchy problem stated. Next the case of spherically symmetric asymptotically flat solutions is examined in detail. The approach taken, using maximal-isotropic coordinates, is new. It is shown that if a singularity occurs in the time evolution of spherically symmetric initial data, the first singularity (as measured by a maximal time coordinate) occurs at the centre. Then it is shown that for small initial data the solution exists globally in time and is geodesically complete. Finally, the proof of the general local existence theorem is sketched. This is intended to be an informal introduction to some of the ideas which are important in proving such theorems rather than a formal proof.

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 Dates: 1997
 Publication Status: Issued
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 Identifiers: eDoc: 331296
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Title: Mathematics of Gravitation : Part I: Lorentzian Geometry and Einstein Equatations
Source Genre: Book
 Creator(s):
Chrusciel, Piotr T., Editor
Affiliations:
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Publ. Info: Warszawa : Polish Academy of Sciences, Institute of Mathematics
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 35 - 68 Identifier: ISSN: 0137-6934

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Title: Banach Center Publications
Source Genre: Series
 Creator(s):
Banach Center, Editor  
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Pages: - Volume / Issue: 41 Sequence Number: - Start / End Page: - Identifier: ISSN: 0137-6934