1996/04/01 by Alan D. Rendall, Rendall, Alan D. · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #Cosmology and Gravitation Theories #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9604001
36 pages. Lectures given at the Banach centre, Warsaw, March 1996
arxiv created 1996/04/01 · openalex publication_date 1996/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.