Local Prescribed Mean Curvature foliations in cosmological spacetimes

A theorem about local in time existence of spacelike foliations with prescribed mean curvature in cosmological spacetimes will be proved. The time function of the foliation is geometrically defined and fixes the diffeomorphism invariance inherent in general foliations of spacetimes. Moreover, in contrast to the situation of the more special constant mean curvature foliations, which play an important role in the global analysis of spacetimes, this theorem overcomes the existence problem arising from topological restrictions for surfaces of constant mean curvature.Comment: 23 pages, no figure

Isotropic cosmological singularities 2: The Einstein-Vlasov system

We consider the conformal Einstein equations for massless collisionless gas cosmologies which admit an isotropic singularity. After developing the general theory, we restrict to spatially-homogeneous cosmologies. We show that the Cauchy problem for these equations is well-posed with data consisting of the limiting particle distribution function at the singularity.Comment: LaTeX, 37 pages, no figures, submitted to Ann. Phy

Defensive realism and the Concert of Europe

Why do great powers expand? Offensive realist John Mearsheimer claims that states wage an eternal struggle for power, and that those strong enough to seek regional hegemony nearly always do. Mearsheimer's evidence, however, displays a selection bias. Examining four crises between 1814 and 1840, I show that the balance of power restrained Russia, Prussia and France. Yet all three also exercised self-restraint; Russia, in particular, passed up chances to bid for hegemony in 1815 and to topple Ottoman Turkey in 1829. Defensive realism gives a better account of the Concert of Europe, because it combines structural realism with non-realist theories of state preferences

Existence of constant mean curvature foliations in spacetimes with two-dimensional local symmetry

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 compact constant mean curvature hypersurface can be covered by a foliation of compact constant mean curvature hypersurfaces. Moreover, the mean curvature of the leaves of this foliation takes on arbitrarily negative values and so the initial singularity in these spacetimes is a crushing singularity. The simplest examples occur when the spatial topology is that of a torus, with the standard global Killing vectors, but more exotic topologies are also covered. In the course of the proof it is shown that in this class of spacetimes a kind of positive mass theorem holds. The symmetry singles out a compact surface passing through any given point of spacetime and the Hawking mass of any such surface is non-negative. If the Hawking mass of any one of these surfaces is zero then the entire spacetime is flat.Comment: 22 page

Constant mean curvature foliations in cosmological spacetimes

Foliations by constant mean curvature hypersurfaces provide a possibility of defining a preferred time coordinate in general relativity. In the following various conjectures are made about the existence of foliations of this kind in spacetimes satisfying the strong energy condition and possessing compact Cauchy hypersurfaces. Recent progress on proving these conjectures under supplementary assumptions is reviewed. The method of proof used is explained and the prospects for generalizing it discussed. The relations of these questions to cosmic censorship and the closed universe recollapse conjecture are pointed out.Comment: 11 pages. Contribution to the Journees Relativiste

The structure of singularities in inhomogeneous cosmological models

Recent progress in understanding the structure of cosmological singularities is reviewed. The well-known picture due to Belinskii, Khalatnikov and Lifschitz (BKL) is summarized briefly and it is discussed what existing analytical and numerical results have to tell us about the validity of this picture. If the BKL description is correct then most cosmological singularities are complicated. However there are some cases where it predicts simple singularities. These cases should be particularly amenable to mathematical investigation and the results in this direction which have been achieved so far are described.Comment: 5 pages, to appear in proceedings of conference on mathematical cosmology, Potsdam, 199

Cosmic Censorship for Some Spatially Homogeneous Cosmological Models

The global properties of spatially homogeneous cosmological models with collisionless matter are studied. It is shown that as long as the mean curvature of the hypersurfaces of homogeneity remains finite no singularity can occur in finite proper time as measured by observers whose worldlines are orthogonal to these hypersurfaces. Strong cosmic censorship is then proved for the Bianchi I, Bianchi IX and Kantowski-Sachs symmetry classes.Comment: 14 pages, Plain TeX, MPA-AR-93-