Second-order light deflection by tidal charged black holes on the brane

We derive the deflection angle of light rays passing near a black hole with mass m and tidal charge q, confined to a generalized Randall-Sundrum brane with co-dimension 1. We employ the weak lensing approach, up to the second order in perturbation theory by two distinct methods. First we adopt a Lagrangian approach and derive the deflection angle from the analysis of the geodesic equations. Then we adopt a Hamiltonian approach and we recover the same result from the analysis of the eikonal. With this we re-establish the unicity of the result as given by the two methods. Our results in turn implies a more rigorous constraint on the tidal charge from solar system measurements, than derived before. © 2009 IOP Publishing Ltd.