Photon motion in Kerr–de Sitter  spacetimes

We study the general motion of photons in the Kerr–de Sitter black-hole and naked singularity spacetimes. The motion is governed by the impact parameters X, related to the axial symmetry of the spacetime, and q, related to its hidden symmetry. Appropriate ‘effective potentials’ governing the latitudinal and radial motion are introduced and their behavior is examined by the ‘Chinese boxes’ technique giving regions allowed for the motion in terms of the impact parameters. Restrictions on the impact parameters X and q are established in dependence on the spacetime parameters $$M, \Lambda , a$$. The motion can be of orbital type (crossing the equatorial plane, $$q>0$$) and vortical type (tied above or below the equatorial plane, $$q