Gravitational Lensing in an Energy-Dependent Spacetime Metric

In this article, we explore the consequences in the calculation of deflection angle of photons, caused by a gravitational source of mass M, for the case of an energy dependent metric. We analyze the corrections to the standard Schwarzschild case for the weak and strong limits. In both cases, the corrections to the deflection angle are of the order ?/E Pl, where E Pl is the Planck energy and ?, the energy of the photon at spatial infinite. The corrections to the angular separation image is also of order ?/E Pl, for the weak limit, while in the strong case there is a corrective term with the shape ?/E Pl n e 2n? for the relativistic image of order n. The amplification of the image is also discussed. Even if corrections are tiny, in both limits, we discuss the qualitative effects for different types of Lorentz invariance deformations. © World Scientific Publishing Company.