494 research outputs found
Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: An exact vacuum solution in five dimensions
As is well-known, Kerr-Schild metrics linearize the Einstein tensor. We shall
see here that they also simplify the Gauss-Bonnet tensor, which turns out to be
only quadratic in the arbitrary Kerr-Schild function f when the seed metric is
maximally symmetric. This property allows us to give a simple analytical
expression for its trace, when the seed metric is a five dimensional maximally
symmetric spacetime in spheroidal coordinates with arbitrary parameters a and
b. We also write in a (fairly) simple form the full Einstein-Gauss-Bonnet
tensor (with a cosmological term) when the seed metric is flat and the
oblateness parameters are equal, a=b. Armed with these results we give in a
compact form the solution of the trace of the Einstein-Gauss-Bonnet field
equations with a cosmological term and a different than b. We then examine
whether this solution for the trace does solve the remaining field equations.
We find that it does not in general, unless the Gauss-Bonnet coupling is such
that the field equations have a unique maximally symmetric solution.Comment: 10 pages, no figures, references added. Last version for CQ
Conserved Charges of Higher D Kerr-AdS Spacetimes
We compute the energy and angular momenta of recent D-dimensional Kerr-AdS
solutions to cosmological Einstein gravity, as well as of the BTZ metric, using
our invariant charge definitions.Comment: 11 pages, references added, equation correcte
Superpotentials from variational derivatives rather than Lagrangians in relativistic theories of gravity
The prescription of Silva to derive superpotential equations from variational
derivatives rather than from Lagrangian densities is applied to theories of
gravity derived from Lovelock Lagrangians in the Palatini representation.
Spacetimes are without torsion and isolated sources of gravity are minimally
coupled. On a closed boundary of spacetime, the metric is given and the
connection coefficients are those of Christoffel. We derive equations for the
superpotentials in these conditions. The equations are easily integrated and we
give the general expression for all superpotentials associated with Lovelock
Lagrangians. We find, in particular, that in Einstein's theory, in any number
of dimensions, the superpotential, valid at spatial and at null infinity, is
that of Katz, Bicak and Lynden-Bell, the KBL superpotential. We also give
explicitly the superpotential for Gauss-Bonnet theories of gravity. Finally, we
find a simple expression for the superpotential of Einstein-Gauss-Bonnet
theories with an anti-de Sitter background: it is minus the KBL superpotential,
confirming, as it should, the calculation of the total mass-energy of spacetime
at spatial infinity by Deser and Tekin.Comment: Scheduled to appear in Class. Quantum Grav. August 200
Brane versus shell cosmologies in Einstein and Einstein-Gauss-Bonnet theories
We first illustrate on a simple example how, in existing brane cosmological
models, the connection of a 'bulk' region to its mirror image creates matter on
the 'brane'. Next, we present a cosmological model with no symmetry which
is a spherical symmetric 'shell' separating two metrically different
5-dimensional anti-de Sitter regions. We find that our model becomes
Friedmannian at late times, like present brane models, but that its early time
behaviour is very different: the scale factor grows from a non-zero value at
the big bang singularity. We then show how the Israel matching conditions
across the membrane (that is either a brane or a shell) have to be modified if
more general equations than Einstein's, including a Gauss-Bonnet correction,
hold in the bulk, as is likely to be the case in a low energy limit of string
theory. We find that the membrane can then no longer be treated in the thin
wall approximation. However its microphysics may, in some instances, be simply
hidden in a renormalization of Einstein's constant, in which cases Einstein and
Gauss-Bonnet membranes are identical.Comment: 15 pages, submitted to Phys. Rev.
Lorentz-violating vs ghost gravitons: the example of Weyl gravity
We show that the ghost degrees of freedom of Einstein gravity with a Weyl
term can be eliminated by a simple mechanism that invokes local Lorentz
symmetry breaking. We demonstrate how the mechanism works in a cosmological
setting. The presence of the Weyl term forces a redefinition of the quantum
vacuum state of the tensor perturbations. As a consequence the amplitude of
their spectrum blows up when the Lorentz-violating scale becomes comparable to
the Hubble radius. Such a behaviour is in sharp contrast to what happens in
standard Weyl gravity where the gravitational ghosts smoothly damp out the
spectrum of primordial gravitational waves.Comment: 14 pages, 3 figures, REVTeX 4.
Conservation Laws and Cosmological Perturbations in Curved Universes
When working in synchronous gauges, pseudo-tensor conservation laws are often
used to set the initial conditions for cosmological scalar perturbations, when
those are generated by topological defects which suddenly appear in an up to
then perfectly homogeneous and isotropic universe. However those conservation
laws are restricted to spatially flat (K=0) Friedmann-Lema\^\i tre spacetimes.
In this paper, we first show that in fact they implement a matching condition
between the pre- and post- transition eras and, in doing so, we are able to
generalize them and set the initial conditions for all . Finally, in the
long wavelength limit, we encode them into a vector conservation law having a
well-defined geometrical meaning.Comment: 15 pages, no figure, to appear in Phys. Rev.
On linearized gravity in the Randall-Sundrum scenario
In the literature about the Randall-Sundrum scenario one finds on one hand
that there exist (small) corrections to Newton's law of gravity on the brane,
and on another that the exact (and henceforth linearized) Einstein equations
can be recovered on the brane. The explanation for these seemingly
contradictory results is that the behaviour of the bulk far from the brane is
different in both models. We show that explicitely in this paper.Comment: 12 pages, plain TeX, no figure
ASYMPTOTIC BEHAVIOR OF COMPLEX SCALAR FIELDS IN A FRIEDMAN-LEMAITRE UNIVERSE
We study the coupled Einstein-Klein-Gordon equations for a complex scalar
field with and without a quartic self-interaction in a curvatureless
Friedman-Lema\^{\i}\-tre Universe. The equations can be written as a set of
four coupled first order non-linear differential equations, for which we
establish the phase portrait for the time evolution of the scalar field. To
that purpose we find the singular points of the differential equations lying in
the finite region and at infinity of the phase space and study the
corresponding asymptotic behavior of the solutions. This knowledge is of
relevance, since it provides the initial conditions which are needed to solve
numerically the differential equations. For some singular points lying at
infinity we recover the expected emergence of an inflationary stage.Comment: uuencoded, compressed tarfile containing a 15 pages Latex file and 2
postscipt figures. Accepted for publication on Phys. Rev.
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