Galactic Metric, Dark Radiation, Dark Pressure, and Gravitational Lensing in Brane World Models

In the brane world scenario, the four-dimensional effective Einstein equation has extra terms that arise from the embedding of the 3-brane in the bulk. These nonlocal effects may provide an explanation for the dynamics of the neutral hydrogen clouds at large distances from the galactic center, which is usually explained by postulating the existence of the dark matter. We obtain the exact galactic metric, the dark radiation, and the dark pressure in the flat rotation curve region in the brane world scenario. Due to the presence of the bulk effects, the flat rotation curves could extend several hundred kiloparsecs. The limiting radius for which bulk effects are important is compared with the numerical values of the truncation parameter of the dark matter halos, obtained from weak-lensing observations. There is a relatively good agreement between the predictions of the model and observations. The deflection of photons in the flat rotation curve region is also considered. The bending angle predicted by the brane world models is much larger than that predicted by dark matter models. The angular radii of the Einstein rings are obtained in the small-angle approximation. The tangential shear is compared with the observational data obtained in the weak lensing of galaxies in the Red-Sequence Cluster Survey. The study of the light deflection by galaxies and the gravitational lensing could discriminate between the different dynamical laws proposed to model the motion of particles at the galactic level and the standard dark matter scenario.