721 research outputs found

### Future complete spacetimes with spacelike isometry group and field sources

We extend to the Einstein Maxwell Higgs system results first obtained
previously in collaboration with V. Moncrief for Einstein equations in vacuum.Comment: to appear in proceedings of the greek relativity meeting 200

### 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
$\beta^{i}(t,x^{j})$ and the spatial scalar potential $\phi(t,x^{j})$,
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 $(t,x^{j})$ 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 $(1)$ taking a further time derivative of the equation
of motion of the canonical momentum, and $(2)$ adding a covariant spatial
derivative of the momentum constraints of general relativity (Lagrange
multiplier $\beta^{i}$) or of the Gauss's law constraint of electromagnetism
(Lagrange multiplier $\phi$). 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

### The Cauchy problem for metric-affine f(R)-gravity in presence of a Klein-Gordon scalar field

We study the initial value formulation of metric-affine f(R)-gravity in
presence of a Klein-Gordon scalar field acting as source of the field
equations. Sufficient conditions for the well-posedness of the Cauchy problem
are formulated. This result completes the analysis of the same problem already
considered for other sources.Comment: 6 page

### 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

### A rigidity theorem for nonvacuum initial data

In this note we prove a theorem on non-vacuum initial data for general
relativity. The result presents a ``rigidity phenomenon'' for the extrinsic
curvature, caused by the non-positive scalar curvature.
More precisely, we state that in the case of asymptotically flat non-vacuum
initial data if the metric has everywhere non-positive scalar curvature then
the extrinsic curvature cannot be compactly supported.Comment: This is an extended and published version: LaTex, 10 pages, no
figure

### Geometrical Well Posed Systems for the Einstein Equations

We show that, given an arbitrary shift, the lapse $N$ can be chosen so that
the extrinsic curvature $K$ of the space slices with metric $\overline g$ in
arbitrary coordinates of a solution of Einstein's equations satisfies a
quasi-linear wave equation. We give a geometric first order symmetric
hyperbolic system verified in vacuum by $\overline g$, $K$ and $N$. We show
that one can also obtain a quasi-linear wave equation for $K$ by requiring $N$
to satisfy at each time an elliptic equation which fixes the value of the mean
extrinsic curvature of the space slices.Comment: 13 pages, latex, no figure

### A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds

We establish new existence and non-existence results for positive solutions
of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This
equation arises from the Hamiltonian constraint equation for the
Einstein-scalar field system in general relativity. Our analysis introduces
variational techniques, in the form of the mountain pass lemma, to the analysis
of the Hamiltonian constraint equation, which has been previously studied by
other methods.Comment: 15 page

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