602 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
A note on the Deser-Tekin charges
Perturbed equations for an arbitrary metric theory of gravity in
dimensions are constructed in the vacuum of this theory. The nonlinear part
together with matter fields are a source for the linear part and are treated as
a total energy-momentum tensor. A generalized family of conserved currents
expressed through divergences of anti-symmetrical tensor densities
(superpotentials) linear in perturbations is constructed. The new family
generalizes the Deser and Tekin currents and superpotentials in quadratic
curvature gravity theories generating Killing charges in dS and AdS vacua. As
an example, the mass of the -dimensional Schwarzschild black hole in an
effective AdS spacetime (a solution in the Einstein-Gauss-Bonnet theory) is
examined.Comment: LATEX, 7 pages, no figure
Kink-antikink, trapping bags and five-dimensional Gauss-Bonnet gravity
Five-dimensional Gauss-Bonnet gravity, with one warped extra-dimension,
allows classes of solutions where two scalar fields combine either in a
kink-antikink system or in a trapping bag configuration. While the
kink-antikink system can be interpreted as a pair of gravitating domain walls
with opposite topological charges, the trapping bag solution consists of a
domain wall supplemented by a non-topological defect. In both classes of
solutions, for large absolute values of the bulk coordinate (i.e. far from the
core of the defects), the geometry is given by five-dimensional anti-de Sitter
space.Comment: 8 pages, 2 figure
On matching conditions for cosmological perturbations
We derive the matching conditions for cosmological perturbations in a
Friedmann Universe where the equation of state undergoes a sharp jump, for
instance as a result of a phase transition. The physics of the transition which
is needed to follow the fate of the perturbations is clarified. We dissipate
misleading statements made recently in the literature concerning the
predictions of the primordial fluctuations from inflation and confirm standard
results. Applications to string cosmology are considered.Comment: 20 pages, latex (revtex), 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.
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
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.
Gravitating multidefects from higher dimensions
Warped configurations admitting pairs of gravitating defects are analyzed.
After devising a general method for the construction of multidefects, specific
examples are presented in the case of higher-dimensional Einstein-Hilbert
gravity. The obtained profiles describe diverse physical situations such as
(topological) kink-antikink systems, pairs of non-topological solitons and
bound configurations of a kink and of a non-topological soliton. In all the
mentioned cases the geometry is always well behaved (all relevant curvature
invariants are regular) and tends to five-dimensional anti-de Sitter space-time
for large asymptotic values of the bulk coordinate. Particular classes of
solutions can be generalized to the framework where the gravity part of the
action includes, as a correction, the Euler-Gauss-Bonnet combination. After
scrutinizing the structure of the zero modes, the obtained results are compared
with conventional gravitating configurations containing a single topological
defect.Comment: 27 pages, 5 included figure
New features of flat (4+1)-dimensional cosmological model with a perfect fluid in Gauss-Bonnet gravity
We investigated a flat multidimensional cosmological model in Gauss-Bonnet
gravity in presence of a matter in form of perfect fluid. We found analytically
new stationary regimes (these results are valid for arbitrary number of spatial
dimensions) and studied their stability by means of numerical recipes in
4+1-dimensional case. In the vicinity of the stationary regime we discovered
numerically another non-singular regime which appears to be periodical.
Finally, we demonstrated that the presence of matter in form of a perfect fluid
lifts some constraints on the dynamics of the 4+1-dimensional model which have
been found earlier.Comment: 14 pages, 5 figures, 1 table; v2 minor corrections, conclusions
unchange
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
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