2,609 research outputs found
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
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-
Asymptotics of solutions of the Einstein equations with positive cosmological constant
A positive cosmological constant simplifies the asymptotics of forever
expanding cosmological solutions of the Einstein equations. In this paper a
general mathematical analysis on the level of formal power series is carried
out for vacuum spacetimes of any dimension and perfect fluid spacetimes with
linear equation of state in spacetime dimension four. For equations of state
stiffer than radiation evidence for development of large gradients, analogous
to spikes in Gowdy spacetimes, is found. It is shown that any vacuum solution
satisfying minimal asymptotic conditions has a full asymptotic expansion given
by the formal series. In four spacetime dimensions, and for spatially
homogeneous spacetimes of any dimension, these minimal conditions can be
derived for appropriate initial data. Using Fuchsian methods the existence of
vacuum spacetimes with the given formal asymptotics depending on the maximal
number of free functions is shown without symmetry assumptions.Comment: 23 page
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
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