**Publication date:** Jul 2000

**Abstract:**

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. It is shown that among all

inertial forces defined within the framework of the optical geometry,

just the centrifugal force plays a fundamental role in connection with

the embedding diagrams because it changes sign at the turning points of

the diagrams. The embedding diagrams do not cover the stationary part of

the Kerr-Newman spacetimes completely. Hence, the limits of

embeddability are given, and it is established which of the photon

circular orbits hosted by the 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. It is shown that embedding diagrams are closely

related to the notion of the radius of gyration which is useful for

analysing a fluid rotating in strong gravitational fields.

**Authors:**

Stuchlík, Z.; Hledík, S.; Jurán, J.;