6,577 research outputs found
Cosmological Singularities and Bel-Robinson Energy
We consider the problem of describing the asymptotic behaviour of
\textsc{FRW} universes near their spacetime singularities in general
relativity. We find that the Bel-Robinson energy of these universes in
conjunction with the Hubble expansion rate and the scale factor proves to be an
appropriate measure leading to a complete classification of the possible
singularities. We show how our scheme covers all known cases of cosmological
asymptotics possible in these universes and also predicts new and distinct
types of singularities. We further prove that various asymptotic forms met in
flat cosmologies continue to hold true in their curved counterparts. These
include phantom universes with their recently discovered big rips, sudden
singularities as well as others belonging to graduated inflationary models.Comment: 20 pages, latex; v2: 21 pages, additions to comply with final
version, to appear in the J. Geom. Phy
Half polarized U(1) symmetric vacuum spacetimes with AVTD behavior
In a previous work, we used a polarization condition to show that there is a
family of U(1) symmetric solutions of the vacuum Einstein equations such that
each exhibits AVTD (Asymptotic Velocity Term Dominated) behavior in the
neighborhood of its singularity. Here we consider the general case of U(1)
bundles and determine a condition, called the half polarization condition,
necessary and sufficient in our context, for AVTD behavior near the
singularity
Geometrical Hyperbolic Systems for General Relativity and Gauge Theories
The evolution equations of Einstein's theory and of Maxwell's theory---the
latter used as a simple model to illustrate the former--- are written in gauge
covariant first order symmetric hyperbolic form with only physically natural
characteristic directions and speeds for the dynamical variables. Quantities
representing gauge degrees of freedom [the spatial shift vector
and the spatial scalar potential ,
respectively] are not among the dynamical variables: the gauge and the physical
quantities in the evolution equations are effectively decoupled. For example,
the gauge quantities could be obtained as functions of from
subsidiary equations that are not part of the evolution equations. Propagation
of certain (``radiative'') dynamical variables along the physical light cone is
gauge invariant while the remaining dynamical variables are dragged along the
axes orthogonal to the spacelike time slices by the propagating variables. We
obtain these results by taking a further time derivative of the equation
of motion of the canonical momentum, and adding a covariant spatial
derivative of the momentum constraints of general relativity (Lagrange
multiplier ) or of the Gauss's law constraint of electromagnetism
(Lagrange multiplier ). General relativity also requires a harmonic time
slicing condition or a specific generalization of it that brings in the
Hamiltonian constraint when we pass to first order symmetric form. The
dynamically propagating gravity fields straightforwardly determine the
``electric'' or ``tidal'' parts of the Riemann tensor.Comment: 24 pages, latex, no figure
Symmetries of distributional domain wall geometries
Generalizing the Lie derivative of smooth tensor fields to
distribution-valued tensors, we examine the Killing symmetries and the
collineations of the curvature tensors of some distributional domain wall
geometries. The chosen geometries are rigorously the distributional thin wall
limit of self gravitating scalar field configurations representing thick domain
walls and the permanence and/or the rising of symmetries in the limit process
is studied. We show that, for all the thin wall spacetimes considered, the
symmetries of the distributional curvature tensors turns out to be the Killing
symmetries of the pullback of the metric tensor to the surface where the
singular part of these tensors is supported. Remarkably enough, for the
non-reflection symmetric domain wall studied, these Killing symmetries are not
necessarily symmetries of the ambient spacetime on both sides of the wall
Motion of Isolated bodies
It is shown that sufficiently smooth initial data for the Einstein-dust or
the Einstein-Maxwell-dust equations with non-negative density of compact
support develop into solutions representing isolated bodies in the sense that
the matter field has spatially compact support and is embedded in an exterior
vacuum solution
Constraints and evolution in cosmology
We review some old and new results about strict and non strict hyperbolic
formulations of the Einstein equations.Comment: To appear in the proceedings of the first Aegean summer school in
General Relativity, S. Cotsakis ed. Springer Lecture Notes in Physic
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