Equatorial photon motion in the Kerr-Newman spacetimes with a non-zero cosmological constant

Discussion of the equatorial photon motion in Kerr-Newman black-hole and na ked-singularity spacetimes with a non-zero cosmological constant is present ed. Both repulsive and attractive cosmological constants are considered. An appropriate 'effective potential' governing the photon radial motion is de fined, circular photon orbits are determined, and their stability with resp ect to radial perturbations is established. The spacetimes are divided into separated classes according to the properties of the 'effective potential' . There is a special class of Kerr-Newman-de Sitter black-hole spacetimes w ith the restricted repulsive barrier. In such spacetimes, photons with high positive End all negative values of their impact parameter can travel free ly between the outerblack-hole horizon and the cosmological horizon due to an interplay between the rotation of the source and the cosmological repuls ion. It is shown that this type of behaviour of the photon motion is connec ted to an unusual relation between the values of the impact parameters of t he photons and their directional angles relative to the outward radial dire ction as measured in the locally non-rotating frames. Surprisingly, some ph otons counterrotating in these frames have a positive impact parameter. Suc h photons can be both escaping or captured in the black-hole spacetimes wit h the restricted repulsive barrier. For the black-hole spacetimes with a st andard, divergent repulsive barrier of the equatorial photon motion, the co unterrotating photons with positive impact parameters must all be captured from the region near the black-hole enter horizon as in the case of Kerr bl ack holes, while they all escape from the region near the cosmological hori zon. Further, the azimuthal motion is discussed and photon trajectories are given in typical situations. It is shown that for some photons with negati ve impact parameter turning points of their azimuthal motion can exist.