13 research outputs found
Linearisation instability of gravity waves?
Gravity waves in irrotational dust spacetimes are characterised by nonzero
magnetic Weyl tensor . In the linearised theory, the divergence of
is set to zero. Recently Lesame et al. [Phys. Rev. D {\bf 53}, 738
(1996)] presented an argument to show that, in the exact nonlinear theory, forces , thus implying a linearisation instability for gravity
waves interacting with matter. However a sign error in the equations
invalidates their conclusion. Bianchi type V spacetimes are shown to include
examples with . An improved covariant formalism is used to
show that in a generic irrotational dust spacetime, the covariant constraint
equations are preserved under evolution. It is shown elsewhere that \mbox{div}
H=0 does not generate further conditions.Comment: 8 pages Revtex; to appear Phys. Rev.
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
Consistency of dust solutions with div H=0
One of the necessary covariant conditions for gravitational radiation is the
vanishing of the divergence of the magnetic Weyl tensor H_{ab}, while H_{ab}
itself is nonzero. We complete a recent analysis by showing that in
irrotational dust spacetimes, the condition div H=0 evolves consistently in the
exact nonlinear theory.Comment: 3 pages Revte
Silent universes with a cosmological constant
We study non-degenerate (Petrov type I) silent universes in the presence of a
non-vanishing cosmological constant L. In contrast to the L=0 case, for which
the orthogonally spatially homogeneous Bianchi type I metrics most likely are
the only admissible metrics, solutions are shown to exist when L is positive.
The general solution is presented for the case where one of the eigenvalues of
the expansion tensor is 0.Comment: 11 pages; several typos corrected which were still present in CGQ
version; minor change
Nonperturbative gravito-magnetic fields
In a cold matter universe, the linearized gravito-magnetic tensor field
satisfies a transverse condition (vanishing divergence) when it is purely
radiative. We show that in the nonlinear theory, it is no longer possible to
maintain the transverse condition, since it leads to a non-terminating chain of
integrability conditions. These conditions are highly restrictive, and are
likely to hold only in models with special symmetries, such as the known
Bianchi and examples. In models with realistic inhomogeneity, the
gravito-magnetic field is necessarily non-transverse at second and higher
order.Comment: Minor changes to match published version; to appear in Phys. Rev.
Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory
The ``Newtonian'' theory of spatially unbounded, self--gravitating,
pressureless continua in Lagrangian form is reconsidered. Following a review of
the pertinent kinematics, we present alternative formulations of the Lagrangian
evolution equations and establish conditions for the equivalence of the
Lagrangian and Eulerian representations. We then distinguish open models based
on Euclidean space from closed models based (without loss of generality)
on a flat torus \T^3. Using a simple averaging method we show that the
spatially averaged variables of an inhomogeneous toroidal model form a
spatially homogeneous ``background'' model and that the averages of open
models, if they exist at all, in general do not obey the dynamical laws of
homogeneous models. We then specialize to those inhomogeneous toroidal models
whose (unique) backgrounds have a Hubble flow, and derive Lagrangian evolution
equations which govern the (conformally rescaled) displacement of the
inhomogeneous flow with respect to its homogeneous background. Finally, we set
up an iteration scheme and prove that the resulting equations have unique
solutions at any order for given initial data, while for open models there
exist infinitely many different solutions for given data.Comment: submitted to G.R.G., TeX 30 pages; AEI preprint 01
Integrability conditions for irrotational dust with a purely electric Weyl tensor: A tetrad analysis
New media and journalism practice in Africa: An agenda for research
Special issue of Journalism: theory, practice and criticism 201