Déflexion de la lumiére et temps de retard à l'échelle cosmologique

Abstract

The research work carried out in this doctoral thesis covers two separate topics. In the Örst topic, we have investigated strong gravitational lensing by a spherically symmetric mass distribution in the framework of two di§erent cosmological models with a positive cosmological constant: The static Kottler (or Schwarzschild-de Sitter) model and the dynamic EinsteinStraus model in the case of áat space (null curvature) and closed space (positive curvature). The Einstein-Straus model consists of a Kottler vacuole embedded in an expanding FriedmanLemaÓtre-Robertson-Walker Universe. The deáection of light and the time delay have been computed in each model then applied to the lensed quasar SDSS J1004+4112. Unlike the case of Kottler model, the analysis of the deáection of light and time delay in both cases of áat and closed Einstein-Straus model have produced results which are in agreement with Rindler and Ishakís claim that a positive cosmological constant attenuates the bending of light. On the other hand, it has been revealed, in the case of closed Einstein-Straus model, that the light bending and time delay decrease considerably as the present scale factor a0 becomes smaller than a limit value about 9:1 1026 m (k0 ' 0:02) highlighting the potential impact of spatial positive curvature. This goes against the Einstein-Straus model in which case the results remain the same regardless of which value is chosen for the present scale factor. Nevertheless, above this limit value ( k0 < 0:02), the obtained results are found to be indistinguishable from the áat case. The second topic revolves around two parts. In the Örst part, we have generalized the generation method of rotating solutions by combining a Önite SU(2; 1) transformations with a Önite coordinate transformation (Önite Geroch transformation). This work seems to show that this generalization would only be apparent. In the second part, a number of problems associated with the Reissner-Nordstrˆm-NUT solution have been explored. We have analyzed in detail the geodesic motion and shown, without assuming time periodicity to make Misner strings unobservable, that the Reissner-Nordstrˆm-NUT spacetime is geodesically complete. Another unpleasant feature of spacetimes with NUTs is the presence of regions containing closed time-like curves. We have shown that among them there are no closed timelike or null geodesics, so the freely falling observers should not encounter causality violations. Considering the motion of electrically charged test particles in the massless magnetically charged Reissner-Nordstrˆm-NUT solution, we Önd that no wordline followed by an initially distant charged particle moving under the action of the Lorentz force can possibly close or self-intersect.