Mario C. Diaz

Solitonic perturbations of perfect fluid Friedmann-Robertson-Walker cosmological models

The authors give a prescription for the application of the inverse scattering generation technique of Belinskii and Zakharov (1978,1979) to perfect fluid cosmological seed solutions in the context of a five-dimensional Kaluza-Klein formalism. As an example they present a two-soliton metric generated from a Friedmann-Robertson-Walker background with a perfect fluid which follows a general gamma-law equation of state. The resulting solution becomes asymptotically the background for large times.

Stochastic processes in cosmology

Abstract The behavior of a radiation filled de Sitter universe in which the equation of state is perturbed by a stochastic term is studied. The corresponding two-dimensional Fokker-Planck equation is solved. The finiteness of the cosmological constant appears to be a necessary condition for the stability of the model which undergoes an exponentially expanding state.

On the geometric structure of nonstationary multisoliton vacuum metrics with real pole trajectories on a general background

We present an analysis of the geometric structure of nonstationary multisoliton vacuum metrics obtained from a general background using the inverse scattering method of Belinsky and Zakharov. In the case of real pole trajectories, in general the algorithm leads, for ann-soliton metric, ton+1 disjoint coordinate patches. We show, by an explicit construction, that each coordinate patch can be smoothly extended to a separate spacetime manifold. As a result we find that there are no shock fronts associated with the pole trajectories and that, contrasting with the situation for pairs of complex pole, there are no structures that can be easily identified with the region of interaction of a given number of solitons.

General solution for slowly-rotating perfect fluid spheres in general relativity

We extend the general prescription of Bergeret al. (1987) for constructing exact solutions of the spherically-symmetric static Einstein equations to the case of slowly rotating spheres.

Smooth extensions of a class of 2n soliton metrics

A particular class of 2n soliton solutions of Einsteins equations, obtained from a flat background by the inverse scattering method of Belinsky and Zakharov, (1978), is considered. Straightforward application of the method leads to metrics whose coefficients are singular along certain hypersurfaces. The geometrical nature of the singularities is analysed. It is found that in some cases they represent curvature singularities. In the other cases they originate only on the choice of coordinates and one can find explicitly smooth extensions through these hypersurfaces. Part of the discussion is restricted to the two soliton metrics, but the results are immediately applicable in the general case.

Brans-Dicke solitons as finite perturbations on perfect-fluid FRW models in general relativity

The authors consider the relation between a class of vacuum solutions in the Brans-Dicke theory of gravitation and perfect barotropic fluid Friedmann-Robertson-Walker cosmologies which can be related to five-dimensional vacuum solutions of Einsteins equations. They present a family of solitonic solutions of the Einstein equations obtained by the application of the inverse scattering technique in five dimensions followed by a subsequent Kaluza-Klein dimensional reduction procedure and a conformal rescaling. The effective energy-momentum tensor that appears is equivalent to that of the Brans-Dicke theory of gravitation. For large time values the metric approaches that of a flat FRW universe with a barotropic perfect fluid as material content. The solutions are a particular case of a family previously presented, together with a new renormalisation procedure for the inverse scattering technique.

Solitonic instabilities in de Sitter universes

Abstract We present three new exact solutions of the four-dimensional Einstein field equations, that can be interpreted as solitonic perturbations of a vacuum de Sitter spacetime, obtained by means of the inverse scattering technique. The solutions are unstable against this type of perturbations, in spite of the fact that they arbitrary small for sufficiently early comoving time. One of the metrics has an energy-momentum tensor that satisfies initially the dominant and strong energy condition and may therefore be relevant to the problem of a precise statement of the cosmic no hair conjecture.