Second-order light deflection by tidal charged black holes on the brane
L. GergelyDepartment of Experimental Physics, University of Szeged, Dóm tér 9, Szeged 6720, HungaryZoltán KeresztesDepartment of Experimental Physics, University of Szeged, Dóm tér 9, Szeged 6720, HungaryMarek DwornikDepartment of Experimental Physics, University of Szeged, Dóm tér 9, Szeged 6720, Hungary
2009en
ABI
Abstract
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.
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