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Local existence and continuation criteria for solutions of the Einstein-Vlasov-scalar field system with surface symmetry
David Tegankong, Norbert Noutchegueme, Alan D. Rendall
We prove in the cases of spherical, plane and hyperbolic symmetry a local in time existence theorem and continuation criteria for cosmological solutions of the Einstein-Vlasov-scal…
The Einstein-Vlasov system
Alan D. Rendall
Rigorous results on solutions of the Einstein-Vlasov system are surveyed. After an introduction to this system of equations and the reasons for studying it, a general discussion of…
Kasner-like behaviour for subcritical Einstein-matter systems
Thibault Damour, Marc Henneaux, Alan D. Rendall +1
Confirming previous heuristic analyses à la Belinskii-Khalatnikov-Lifshitz, it is rigorously proven that certain ``subcritical'' Einstein-matter systems exhibit a monotone, general…
Quiescent cosmological singularities
Lars Andersson
I discuss recent work (gr-qc/0001047) on non-oscillatory singularities in four dimensional space-times with scalar field or stiff fluid matter, in the context of the BKL proposal.
Blow-up for solutions of hyperbolic PDE and spacetime singularities
Alan D. Rendall
An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essential…
The structure of singularities in inhomogeneous cosmological models
Alan D. Rendall
Recent progress in understanding the structure of cosmological singularities is reviewed. The well-known picture due to Belinskii, Khalatnikov and Lifschitz (BKL) is summarized bri…