Strong-field gravitational lensing by a Kerr black hole

We consider a Kerr black hole acting as a gravitational deflector in the strong-field regime within the geometrical optics and point source approximations. The Kerr black-hole gravitational lens geometry consists of an observer and a source located far away and placed at arbitrary inclinations with respect to the black hole's equatorial plane. For this geometry the null geodesics equations of our interest can go around the black hole several times before reaching the observer. Such photon trajectories are written in terms of the angular Positions in the obzerver's sky and therefore become lens equations. By performing an analysis of the null geodesic motion off the Kerr black-hole equatorial plane we found for any image a simple classification scheme based on two integers numbers: the number of turning points in the polar coordinate theta, and the number of windings around the black hole's rotation axis. As a numerical application, we consider a supermassive Kerr black hole at the galactic center as a gravitational deflector. In this case, we show that our proposed computational and graphical scheme to solve the lens equations works successfully by calculating the positions and magnifications of the relativistic images for different source-observer geometries. In particular, we consider observers located near the Kerr black-hole equatorial plane, at the poles, and at an angle of pi/4.