1,145 research outputs found
Static self-gravitating elastic bodies in Einstein gravity
We prove that given a stress-free elastic body there exists, for sufficiently
small values of the gravitational constant, a unique static solution of the
Einstein equations coupled to the equations of relativistic elasticity. The
solution constructed is a small deformation of the relaxed configuration. This
result yields the first proof of existence of static solutions of the Einstein
equations without symmetries.Comment: 29 pages. Updated to conform with published version, typos fixe
On unbounded bodies with finite mass: asymptotic behaviour
There is introduced a class of barotropic equations of state (EOS) which
become polytropic of index 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
Rotating elastic bodies in Einstein gravity
We prove that, given a stress-free, axially symmetric elastic body, there
exists, for sufficiently small values of the gravitational constant and of the
angular frequency, a unique stationary axisymmetric solution to the Einstein
equations coupled to the equations of relativistic elasticity with the body
performing rigid rotations around the symmetry axis at the given angular
frequency.Comment: 27 page
TT-tensors and conformally flat structures on 3-manifolds
We study transverse-tracefree (TT)-tensors on conformally flat 3-manifolds
. The Cotton-York tensor linearized at 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 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
, the resulting tensor fields on
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
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