Gravitational deflection of light in interior Schwarzschild metric

We determine the angle of deflection of light by the gravitational field inside and outside a spherical body with a homogeneous mass density. We show that the largest deflections, which can be measured by weak gravitational lensing, are in a region displaced from the center of mass. This result can be extended to more general distributions of matter. This displacement, observed in galaxies and colliding galaxy clusters, may be therefore explained without dark matter, within general relativity.