Parameter constraints from shadows of Kerr-Newman-dS black holes with cloud strings and quintessence

The motion of photons around the Kerr-Newman-dS black hole surrounded by quintessence and a cloud of strings is investigated. The existence of the Carter constant leads to that of unstable circular photon orbits on a two-dimensional plane not limited to the equatorial plane and unstable spherical photon orbits in the three-dimensional space. These circular or spherical photon orbits can determine two impact parameters, which are used to calculate black hole shadows. For the case of a spherically symmetric nonrotating black hole, the black hole shadow is circular and its size is independent of an observation angle and a plane on which a circular photon orbit exists. The shadow sizes are significantly influenced by the parameters involving the cloud of strings, quintessence parameter, magnitude of quintessential state parameter, and cosmological constant. When the black hole is spinning and axially symmetric, the black hole shadow is dependent on the observation angle. The effects of the parameters excluding the spin parameter on the sizes of black hole shadows in the rotating case are similar to those in the nonrotating case. Based on the Event Horizon Telescope observations of M87*, the constraint of the curvature radius is used to constrain these parameters. For slowly rotating black holes, the allowed regions of the parameters including the cosmological constant are given.