577 research outputs found
Collapsing sphere on the brane radiates
We study the analogue of the Oppenheimer-Snyder model of a collapsing sphere
of homogeneous dust on the Randall-Sundrum type brane. We show that the
collapsing sphere has the Vaidya radiation envelope which is followed by the
brane analogue of the Schwarzschild solution described by the
Reissner-Nordstrom metric. The collapsing solution is matched to the brane
generalized Vaidya solution and which in turn is matched to the
Reissner-Nordstrom metric. The mediation by the Vaidya radiation zone is the
new feature introduced by the brane. Since the radiating mediation is
essential, we are led to the remarkable conclusion that a collapsing sphere on
the brane does indeed, in contrast to general relativity, radiate null
radiation.Comment: Minor changes, main results remain unchanged, to appear in Phys.
Lett.
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
Mass and angular momenta of Kerr anti-de Sitter spacetimes in Einstein-Gauss-Bonnet theory
We compute the mass and angular momenta of rotating anti-de Sitter spacetimes
in Einstein-Gauss-Bonnet theory of gravity using a superpotential derived from
standard Noether identities. The calculation relies on the fact that the
Einstein and Einstein-Gauss-Bonnet vacuum equations are the same when
linearized on maximally symmetric backgrounds and uses the recently discovered
D-dimensional Kerr-anti-de Sitter solutions to Einstein's equations
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
Non-topological gravitating defects in five-dimensional anti-de Sitter space
A class of five-dimensional warped solutions is presented. The geometry is
everywhere regular and tends to five-dimensional anti-de Sitter space for large
absolute values of the bulk coordinate. The physical features of the solutions
change depending on the value of an integer parameter. In particular, a set of
solutions describes generalized gravitating kinks where the scalar field
interpolates between two different minima of the potential. The other category
of solutions describes instead gravitating defects where the scalar profile is
always finite and reaches the same constant asymptote both for positive and
negative values of the bulk coordinate. In this sense the profiles are
non-topological. The physical features of the zero modes are discussed.Comment: 9 pages, 4 figure
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
Normal modes for metric fluctuations in a class of higher-dimensional backgrounds
We discuss a gauge invariant approach to the theory of cosmological
perturbations in a higher-dimensonal background. We find the normal modes which
diagonalize the perturbed action, for a scalar field minimally coupled to
gravity, in a higher-dimensional manifold M of the Bianchi-type I, under the
assumption that the translations along an isotropic spatial subsection of M are
isometries of the full, perturbed background. We show that, in the absence of
scalar field potential, the canonical variables for scalar and tensor metric
perturbations satisfy exactly the same evolution equation, and we discuss the
possible dependence of the spectrum on the number of internal dimensions.Comment: 19 pages, LATEX, an explicit example is added to discuss the possible
dependence of the perturbation spectrum on the number of internal dimensions.
To apper in Class. Quantum Gra
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
On the mass of a Kerr-anti-de Sitter spacetime in D dimensions
We show how to compute the mass of a Kerr-anti-de Sitter spacetime with
respect to the anti-de Sitter background in any dimension, using a
superpotential which has been derived from standard Noether identities. The
calculation takes no account of the source of the curvature and confirms
results obtained for black holes via the first law of thermodynamics.Comment: minor changes; accepted by CQ
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.
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