Optical reference geometry of Kerr-Newman spacetimes

Properties of the optical reference geometry related to Kerr-Newman black-h ole and naked-singularity spacetimes are illustrated using embedding diagra ms of their equatorial plane. It is shown that among all inertial forces de fined within the framework of the optical geometry, just the centrifugal fo rce plays a fundamental role in connection with the embedding diagrams beca use it changes sign at the turning points of the diagrams. The embedding di agrams do not cover the stationary part of the Kerr-Newman spacetimes compl etely. Hence, the limits of embeddability are given, and it is established which of the photon circular orbits hosted by the Kerr-Newman spacetimes ap pear in the embeddable regions. Some typical embedding diagrams are constru cted, and the Kerr-Newman backgrounds are classified according to the numbe r of embeddable regions of the optical geometry as well as the number of th eir turning points. It is shown that embedding diagrams are closely related to the notion of the radius of gyration which is useful for analysing a fl uid rotating in strong gravitational fields.