362 research outputs found
Irrotational dust with Div H=0
For irrotational dust the shear tensor is consistently diagonalizable with
its covariant time derivative: , if
and only if the divergence of the magnetic part of the Weyl tensor vanishes:
. We show here that in that case, the consistency of the Ricci
constraints requires that the magnetic part of the Weyl tensor itself vanishes:
.Comment: 19 pages. Latex. Also avaliable at
http://shiva.mth.uct.ac.za/preprints/text/lesame2.te
Horizon area bound and MOTS stability in locally rotationally symmetric solutions
In this paper, we study the stability of marginally outer trapped surfaces
(MOTS), foliating horizons of the form , embedded in locally
rotationally symmetric class II perfect fluid spacetimes. An upper bound on the
area of stable MOTS is obtained. It is shown that any stable MOTS of the types
considered in these spacetimes must be strictly stably outermost, that is,
there are no MOTS ``outside" of and homologous to . Aspects of the
topology of the MOTS, as well as the case when an extension is made to
imperfect fluids, are discussed. Some non-existence results are also obtained.
Finally, the ``growth" of certain matter and curvature quantities on certain
unstable MOTS are provided under specified conditions.Comment: 21 pages, Submitted to CQG, comments are welcom
Shear-Free Gravitational Waves in an Anisotropic Universe
We study gravitational waves propagating through an anisotropic Bianchi I
dust-filled universe (containing the Einstein-de-Sitter universe as a special
case). The waves are modeled as small perturbations of this background
cosmological model and we choose a family of null hypersurfaces in this
space-time to act as the histories of the wavefronts of the radiation. We find
that the perturbations we generate can describe pure gravitational radiation if
and only if the null hypersurfaces are shear-free. We calculate the
gauge-invariant small perturbations explicitly in this case. How these differ
from the corresponding perturbations when the background space-time is
isotropic is clearly exhibited.Comment: 32 pages, accepted for publication in Physical Review
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