455 research outputs found

### On unbounded bodies with finite mass: asymptotic behaviour

There is introduced a class of barotropic equations of state (EOS) which
become polytropic of index $n = 5$ at low pressure. One then studies
asymptotically flat solutions of the static Einstein equations coupled to
perfect fluids having such an EOS. It is shown that such solutions, in the same
manner as the vacuum ones, are conformally smooth or analytic at infinity, when
the EOS is smooth or analytic, respectively.Comment: 6 page

### TT-tensors and conformally flat structures on 3-manifolds

We study transverse-tracefree (TT)-tensors on conformally flat 3-manifolds
$(M,g)$. The Cotton-York tensor linearized at $g$ maps every symmetric
tracefree tensor into one which is TT. The question as to whether this is the
general solution to the TT-condition is viewed as a cohomological problem
within an elliptic complex first found by Gasqui and Goldschmidt and reviewed
in the present paper. The question is answered affirmatively when $M$ is simply
connected and has vanishing 2nd de Rham cohomology.Comment: 11 page

### Bowen-York Tensors

There is derived, for a conformally flat three-space, a family of linear
second-order partial differential operators which send vectors into tracefree,
symmetric two-tensors. These maps, which are parametrized by conformal Killing
vectors on the three-space, are such that the divergence of the resulting
tensor field depends only on the divergence of the original vector field. In
particular these maps send source-free electric fields into TT-tensors.
Moreover, if the original vector field is the Coulomb field on
$\mathbb{R}^3\backslash \lbrace0\rbrace$, the resulting tensor fields on
$\mathbb{R}^3\backslash \lbrace0\rbrace$ are nothing but the family of
TT-tensors originally written down by Bowen and York.Comment: 12 pages, Contribution to CQG Special Issue "A Spacetime Safari:
Essays in Honour of Vincent Moncrief

### The isometry groups of asymptotically flat, asymptotically empty space-times with timelike ADM four-momentum

We give a complete classification of all connected isometry groups, together
with their actions in the asymptotic region, in asymptotically flat,
asymptotically vacuum space--times with timelike ADM four--momentum.Comment: Latex with amssymb, 16 page

### Celestial mechanics of elastic bodies

We construct time independent configurations of two gravitating elastic
bodies. These configurations either correspond to the two bodies moving in a
circular orbit around their center of mass or strictly static configurations.Comment: 16 pages, 2 figures, several typos removed, erratum appeared in
MathZ.263:233,200

### Initial Data for General Relativity with Toroidal Conformal Symmetry

A new class of time-symmetric solutions to the initial value constraints of
vacuum General Relativity is introduced. These data are globally regular,
asymptotically flat (with possibly several asymptotic ends) and in general have
no isometries, but a $U(1)\times U(1)$ group of conformal isometries. After
decomposing the Lichnerowicz conformal factor in a double Fourier series on the
group orbits, the solutions are given in terms of a countable family of
uncoupled ODEs on the orbit space.Comment: REVTEX, 9 pages, ESI Preprint 12

### Helical Solutions in Scalar Gravity

We construct solutions, for small values of $G$ and angular frequency
$\Omega$, of special relativistic scalar gravity coupled to ideally elastic
matter which have helical but no stationary or axial symmetry. They correspond
to a body without any symmetries in steady rotation around one of its axes of
inertia, or two bodies moving on a circle around their center of gravity. Our
construction is rigorous, but modulo an unproved conjecture on the
differentiability of a certain functional.Comment: 11 page

### Initial data for stationary space-times near space-like infinity

We study Cauchy initial data for asymptotically flat, stationary vacuum
space-times near space-like infinity. The fall-off behavior of the intrinsic
metric and the extrinsic curvature is characterized. We prove that they have an
analytic expansion in powers of a radial coordinate. The coefficients of the
expansion are analytic functions of the angles. This result allow us to fill a
gap in the proof found in the literature of the statement that all
asymptotically flat, vacuum stationary space-times admit an analytic
compactification at null infinity. Stationary initial data are physical
important and highly non-trivial examples of a large class of data with similar
regularity properties at space-like infinity, namely, initial data for which
the metric and the extrinsic curvature have asymptotic expansion in terms of
powers of a radial coordinate. We isolate the property of the stationary data
which is responsible for this kind of expansion.Comment: LaTeX 2e, no figures, 12 page

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