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

TL;DR

This paper calculates the second-order light deflection angle caused by tidal charged black holes on a brane, using two methods, and refines constraints on tidal charge from Solar System data.

Contribution

It provides a rigorous derivation of light deflection by tidal charged black holes using both Lagrangian and Hamiltonian approaches, confirming the results and improving tidal charge constraints.

Findings

Derived second-order deflection angle using two methods

Confirmed the unicity of the deflection angle result

Provided tighter constraints on tidal charge from Solar System data

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 codimension one. 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 rigurous constraint on the tidal charge from Solar System measurements, then derived before.