Gravitational Lensing by Black Holes: A Comprehensive Treatment and the Case of the Star S2

Light rays passing very close to a black hole may experience very strong deviations. Two geometries have been separately considered in recent literature: a source behind the black hole (standard gravitational lensing) and a source in front of the black hole (retrolensing). In this paper we start from the strong-field limit approach to recover both situations under the same formalism, describing not only the two geometries just mentioned but also any possible intermediate configurations of the source-lens-observer system without any small-angle limitations. This is done for any spherically symmetric black holes and for the equatorial plane of Kerr black holes. In light of this formalism we revisit the previous literature on retrolensing, sensibly improving the observational estimates. In particular, for the case of the star S2, we give precise predictions for the magnitude of the relativistic images and the time of their highest brightness, which should occur at the beginning of A.D. 2018. The observation of such images would open fascinating perspectives on the measure of the physical parameters of the central black hole, including mass, spin, and distance.