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Properties of the optical reference geometry related to Kerr-Newmanblack-hole and naked-singularity spacetimes are illustrated using embeddingdiagrams of their equatorial plane. Among all inertial forces defined in theframework of the optical geometry, just the centrifugal force plays afundamental role in connection to the embedding diagrams because it changessign at the turning points of the diagrams. The limits of embeddability aregiven, and it is established which of the photon circular orbits hosted the byKerr-Newman spacetimes appear in the embeddable regions. Some typical embeddingdiagrams are constructed, and the Kerr-Newman backgrounds are classifiedaccording to the number of embeddable regions of the optical geometry as wellas the number of their turning points. Embedding diagrams are closely relatedto the notion of the radius of gyration which is useful for analyzing fluidrotating in strong gravitational fields.

Optical reference geometry of the Kerr-Newman spacetimes