1,859 research outputs found
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
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
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
Easy plane baby skyrmions
The baby Skyrme model is studied with a novel choice of potential, . This "easy plane" potential vanishes at the equator of the target
two-sphere. Hence, in contrast to previously studied cases, the boundary value
of the field breaks the residual SO(2) internal symmetry of the model.
Consequently, even the unit charge skyrmion has only discrete symmetry and
consists of a bound state of two half lumps. A model of long-range
inter-skyrmion forces is developed wherein a unit skyrmion is pictured as a
single scalar dipole inducing a massless scalar field tangential to the vacuum
manifold. This model has the interesting feature that the two-skyrmion
interaction energy depends only on the average orientation of the dipoles
relative to the line joining them. Its qualitative predictions are confirmed by
numerical simulations. Global energy minimizers of charges B=1,...,14,18,32 are
found numerically. Up to charge B=6, the minimizers have 2B half lumps
positioned at the vertices of a regular 2B-gon. For charges B >= 7, rectangular
or distorted rectangular arrays of 2B half lumps are preferred, as close to
square as possible.Comment: v3: replaced with journal version, one new reference, one deleted
reference; 8 pages, 5 figures v2: fixed some typos and clarified the
relationship with condensed matter systems 8 pages, 5 figure
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
Cosmological spacetimes not covered by a constant mean curvature slicing
We show that there exist maximal globally hyperbolic solutions of the
Einstein-dust equations which admit a constant mean curvature Cauchy surface,
but are not covered by a constant mean curvature foliation.Comment: 11 page
Einstein and Yang-Mills theories in hyperbolic form without gauge-fixing
The evolution of physical and gauge degrees of freedom in the Einstein and
Yang-Mills theories are separated in a gauge-invariant manner. We show that the
equations of motion of these theories can always be written in
flux-conservative first-order symmetric hyperbolic form. This dynamical form is
ideal for global analysis, analytic approximation methods such as
gauge-invariant perturbation theory, and numerical solution.Comment: 12 pages, revtex3.0, no figure
Slice Energy and Theories of Gravitation
We review recent work on the use of the slice energy concept in generalized
theories of gravitation. We focus on two special features in these theories,
namely, the energy exchange between the matter component and the scalar field
generated by the conformal transformation to the Einstein frame of such
theories and the issue of the physical equivalence of different conformal frame
representations. We show that all such conformally-related, generalized
theories of gravitation allow for the slice energy to be invariably defined and
its fundamental properties be insensitive to conformal transformations.Comment: 16 pages, In: Proceedings of the 11th Greek Relativity Meetin
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
Hamiltonian Time Evolution for General Relativity
Hamiltonian time evolution in terms of an explicit parameter time is derived
for general relativity, even when the constraints are not satisfied, from the
Arnowitt-Deser-Misner-Teitelboim-Ashtekar action in which the slicing density
is freely specified while the lapse is not.
The constraint ``algebra'' becomes a well-posed evolution system for the
constraints; this system is the twice-contracted Bianchi identity when
. The Hamiltonian constraint is an initial value constraint which
determines and hence , given .Comment: 4 pages, revtex, to appear in Phys. Rev. Let
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