The black hole as a gravitational ‘‘lens’’

We discuss the ‘‘images’’ formed when the light from a distant source suffers a large deflection in the intense gravitational field in the immediate vicinity of a Schwarzschild black hole. The light can circle around the black hole one or several times, and therefore give rise to a sequence of images. We show that the deflection angles and the intensities of the images can be expressed in terms of elliptic integrals, leading to simple approximations in the limiting case of very large deflection angles.