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Cosmological solutions of the Einstein-Vlasov system

Friday 16th September 2005 - 14:30 to 15:30
INI Seminar Room 1

I will present some of the global results that have been proved in recent years for the Einstein-Vlasov system in the cosmological case. These results are all obtained under symmetry assumptions and require that spacetime admits an $N$-dimensional symmetry group where $N\geq 2.$ I will mainly focus on the cases $N=2$ and $N=3.$ These situations are rather different since only if $N=2,$ gravitational waves are admitted. The question of global existence is quite well-understood but other important global issues are still open. In the last couple of years studies including a cosmological constant $\Lambda$ or a scalar field have been carried out in cases where $N\geq 3.$ In particular, future geodesic completeness has been proved when $\Lambda>0,$ which is an open problem in the case $\Lambda=0.$

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons