Strong Deflection Limit Lensing Effects in the Minimal Geometric Deformation and Casadio-Fabbri-Mazzacurati Solutions

In this paper we apply the strong deflection limit approach to investigate the gravitational lensing phenomena beyond general relativity. This is accomplished by considering the lensing effects related to black hole solutions that emerge out of the domain of Einstein gravity, namely, the ones acquired from the method of geometric deformation and the Casadio-Fabbri-Mazzacurati brane-world black holes. The lensing observables, for those brane-world black hole metrics, are compared with the standard ones for the Schwarzschild case. We prove that brane-world black holes could have significantly different observational signatures, compared to the Schwarzschild black hole, with terms containing the post-Newtonian parameter, for the case of the Casadio-Fabbri-Mazzacurati, and terms with variable brane-world tension, for the method of geometric deformation.