Optical reference geometry of Kerr-Newman spacetimes

Abstract

Properties of the optical reference geometry related toKerr-Newmanblack-hole and naked-singularity spacetimes are illustrated usingembedding diagrams of their equatorial plane. It is shown that among allinertial forces defined within the framework of the optical geometry, justthe centrifugal force plays a fundamental role in connectionwith theembedding diagrams because it changes sign at the turning points of thediagrams. The embedding diagrams do not cover the stationary part of theKerr-Newman spacetimes completely. Hence, the limits of embeddabilityare given, and it is established which of the photon circular orbitshosted bythe Kerr-Newman spacetimes appear in the embeddableregions.Some typical embedding diagrams are constructed, and the Kerr-Newmanbackgrounds are classified according to the number of embeddable regionsof the optical geometry as well as the number of their turning points.It is shown that embedding diagrams are closely related to the notion ofthe radius of gyration which is useful for analysing afluid rotating instrong gravitational fields.