Francesc Fayos

On the extension of Vaidya and Vaidya-Reissner-Nordström spacetimes

A revision of Israels extension of Vaidyas spacetime is proposed in order to apply the procedure to more general spacetimes. Israels procedure is reformulated to obtain the extension even if the only available function is the mass in the non-extended region. The additional demands on analiticity and energy conditions are discussed. Eventually, the method is applied to the extension of Vaidya-Reissner-Nordstroms spacetime. The different cases arising are described and their conformal diagrams presented.

Matching of the Vaidya and Robertson-Walker metric

The authors give the necessary conditions for the matching of a general Robertson-Walker geometry to general spherically symmetric radiating metric. They also found the conditions for the matching of a Vaidya metric (1951) to a general Robertson-Walker metric. The possible applications of the results to the stellar collapse and to the study of local inhomogeneities in a cosmological context are considered. An alternative interpretation of the energy-momentum tensor of the Robertson-Walker part of spacetime is given in such a way that the physical processes can be better understood.

On the Papapetrou field in vacuum

In this paper we study the electromagnetic fields generated by a Killing vector field in vacuum spacetimes (Papapetrou fields). The motivation of this work is to provide new tools for the resolution of Maxwells equations as well as for the search, characterization, and study of exact solutions of Einsteins equations. The first part of this paper is devoted to an algebraic study in which we give an explicit and covariant procedure to construct the principal null directions of a Papapetrou field. In the second part, we focus on the main differential properties of the principal directions, studying when they are geodesic, and in that case we compute their associated optical scalars. With this information we get the conditions that a principal direction of the Papapetrou field must satisfy in order to be aligned with a multiple principal direction of the Weyl tensor in the case of algebraically special vacuum spacetimes. Finally, we illustrate this study using the Kerr, Kasner and pp waves spacetimes.

General approach to the study of vacuum spacetimes with an isometry

In vacuum spacetimes the exterior derivative of a Killing vector field is a 2-form (called here the Papapetrou field) that satisfies Maxwells equations without electromagnetic sources. In this paper, using the algebraic structure of the Papapetrou field, we will set up a new formalism for the study of vacuum spacetimes with an isometry, which is suitable to investigate the connections between the isometry and the Petrov type of the spacetime. This approach has some advantages, among which are that it leads to a new classification of these spacetimes and the integrability conditions provide expressions that determine the Weyl curvature completely. These facts make the formalism useful for application to any problem or situation with an isometry and requiring the knowledge of the curvature.

Consequences of a Killing symmetry in spacetime's local structure

In this paper we discuss the consequences of a Killing symmetry on the local geometrical structure of four-dimensional spacetimes. We have adopted the point of view introduced in recent works where the exterior derivative of the Killing plays a fundamental role. Then, we study some issues related to this approach and clarify why in many circumstances its use has advantages with respect to other approaches. We also extend the formalism developed in the case of vacuum spacetimes to the general case of an arbitrary energy–momentum content. Finally, we illustrate our framework with the case of spacetimes with a gravitating electromagnetic field.

Spherically symmetric models for stars and voids II: constraints on the radial pressures

We analyse the physical implications of the energy and matching conditions that take part in the construction of spherically symmetric models for stars and voids. We find an important condition on the radial pressures that can be of relevance, for instance, in the modellization of voids in the universe. In this way we show, among other results, that some models for the universe could not possess viable voids. The condition is also applied in order to construct charged radiating stellar models.

VACUUM SPACETIMES WITH AN ISOMETRY

In vacuum space-times the exterior derivative of a Killing vector field is a two-form that satisfies Maxwell equations without electromagnetic sources. Using the algebraic structure of this two-form we have set up a new formalism for the study of vacuum space-times with an isometry.