  Properties of the optical reference geometry related to Kerr-Newman
black-hole and naked-singularity spacetimes are illustrated using embedding
diagrams of their equatorial plane. Among all inertial forces defined in the
framework of the optical geometry, just the centrifugal force plays a
fundamental role in connection to the embedding diagrams because it changes
sign at the turning points of the diagrams. The limits of embeddability are
given, and it is established which of the photon circular orbits hosted the by
Kerr-Newman spacetimes appear in the embeddable regions. Some typical embedding
diagrams are constructed, and the Kerr-Newman backgrounds are classified
according to the number of embeddable regions of the optical geometry as well
as the number of their turning points. Embedding diagrams are closely related
to the notion of the radius of gyration which is useful for analyzing fluid
rotating in strong gravitational fields.
