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

Time-dependent gravitating solitons in five dimensional warped space-times

Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra-dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between two five-dimensional anti-de Sitter space-times for fixed value of the conformal time coordinate. Time dependent solutions containing both topological and non-topological sectors are also obtained. Supplementary degrees of freedom can be also included and, in this case, the resulting multi-soliton solutions may describe time-dependent kink-antikink systems.Comment: 19 pages, 10 figure

A note on the Deser-Tekin charges

Perturbed equations for an arbitrary metric theory of gravity in $D$ 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 $D$-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

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

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.

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

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.

Creation of a brane world with Gauss-Bonnet term

We study a creation of a brane world using an instanton solution. We analyze a brane model with a Gauss-Bonnet term in a bulk spacetime. The curvature of 3-brane is assumed to be closed, flat, or open. We construct instanton solutions with branes for those models, and calculate the value of the actions to discuss an initial state of a brane universe.Comment: 9 pages, 10 figure

Inhomogeneity of Spatial Curvature for Inflation

We study how the initial inhomogeneities of the spatial curvature affect the onset of inflation in the closed universe. We consider a cosmological model which contains a radiation and a cosmological constant. In order to treat the inhomogeneities in the closed universe, we improve the long wavelength approximation such that the non-small spatial curvature is tractable in the lowest order. Using the improved scheme, we show how large inhomogeneities of the spatial curvature prevent the occurrence of inflation.Comment: 17 pages, revtex, 6 figures included using eps