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In the braneworld scenario, the four dimensional effective Einstein equationhas extra terms which arise from the embedding of the 3-brane in the bulk.These non-local effects, generated by the free gravitational field of the bulk,may provide an explanation for the dynamics of the neutral hydrogen clouds atlarge distances from the galactic center, which is usually explained bypostulating the existence of the dark matter. We obtain the exact galacticmetric, the dark radiation and the dark pressure in the flat rotation curvesregion in the brane world scenario. Due to the presence of the bulk effects,the flat rotation curves could extend several hundred kpc. The limiting radiusfor which bulk effects are important is estimated and compared with thenumerical values of the truncation parameter of the dark matter halos, obtainedfrom weak lensing observations. There is a relatively good agreement betweenthe predictions of the model and observations. The deflection of photons isalso considered and the bending angle of light is computed. The bending anglepredicted by the brane world models is much larger than that predicted bystandard general relativistic and dark matter models. The angular radii of theEinstein rings are obtained in the small angles approximation. The predictionsof the brane world model for the tangential shear are compared with theobservational data obtained in the weak lensing of galaxies in the Red-SequenceCluster Survey. Therefore the study of the light deflection by galaxies and thegravitational lensing could discriminate between the different dynamical lawsproposed to model the motion of particles at the galactic level and thestandard dark matter models.Comment: 33 pages, 3 figures, accepted for publication in Ap

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