Conditions for inflation in an initially inhomogeneous universe

Using a long wavelength iteration scheme to solve Einstein's equations near the Big-Bang singularity of a universe driven by a massive scalar field, we find how big initial quasi-isotropic inhomogeneities can be before they can prevent inflation to set in.Comment: 9 pages, plain Tex, gr-qc/yymmnn

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

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

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

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

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

A Rigorous Treatment of Energy Extraction from a Rotating Black Hole

The Cauchy problem is considered for the scalar wave equation in the Kerr geometry. We prove that by choosing a suitable wave packet as initial data, one can extract energy from the black hole, thereby putting supperradiance, the wave analogue of the Penrose process, into a rigorous mathematical framework. We quantify the maximal energy gain. We also compute the infinitesimal change of mass and angular momentum of the black hole, in agreement with Christodoulou's result for the Penrose process. The main mathematical tool is our previously derived integral representation of the wave propagator.Comment: 19 pages, LaTeX, proof of Propositions 2.3 and 3.1 given in more detai

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 $K$. 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 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