Gravitational lensing in the strong field limit

We provide an analytic method to discriminate among different types of black holes on the grounds of their strong field gravitational lensing properties. We expand the deflection angle of the photon in the neighborhood of complete capture, defining a strong field limit, in opposition to the standard weak field limit. This expansion is worked out for a completely generic spherically symmetric spacetime, without any reference to the field equations and just assuming that the light ray follows the geodesics equation. We prove that the deflection angle always diverges logarithmically when the minimum impact parameter is reached. We apply this general formalism to Schwarzschild, Reissner-Nordstr\"om, and…