Photon spherical orbits around a Kerr black hole

Abstract Black holes are trapped spacetime regions. Their inexorable gravitational attraction determines that nothing – not even light – may escape from this region. Thus, a black hole cannot be directly observed. It must be studied by the way it influences the motion of matter particles and light rays in its neighborhood. These trajectories are determined (within a certain approximation) by the black hole geometry's geodesics. In particular, null geodesics – those followed by light rays – possess considerable astrophysical interest: they represent how the radiation emitted around the black hole, or incoming from far away sources, is distorted by the black hole. In this work we present the equations of motion of light rays in the Kerr geometry, that describes a rotating black hole, making use of Hamilton-Jacobi theory. Subsequently, we analyze the conditions for the existence of spherical photon orbits around the black hole. These orbits, representing strong light bending, are the key to determine the optical appearance of the black hole. Finally, using computational methods, we exhibit plots illustrating some of these trajectories.