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Existence and non-existence results for global constant mean curvature foliations
Alan D. Rendall
The main result of this paper is a proof that there are examples of spatially compact solutions of the Einstein-dust equations which only exist for an arbitrarily small amount of C…
Constant mean curvature foliations in cosmological spacetimes
Alan D. Rendall
Foliations by constant mean curvature hypersurfaces provide a possibility of defining a preferred time coordinate in general relativity. In the following various conjectures are ma…
Existence of constant mean curvature foliations in spacetimes with two-dimensional local symmetry
Alan D. Rendall
It is shown that in a class of maximal globally hyperbolic spacetimes admitting two local Killing vectors, the past (defined with respect to an appropriate time orientation) of any…
An introduction to the Einstein-Vlasov system
Alan D. Rendall
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 a…