Optical reference geometry of the Kerr-Newman spacetimes

TL;DR

This paper explores the optical reference geometry of Kerr-Newman spacetimes, analyzing embedding diagrams, inertial forces, and the classification of these spacetimes based on embeddability and turning points.

Contribution

It provides a detailed analysis of the embeddability limits, the role of centrifugal force, and classifies Kerr-Newman spacetimes by their optical geometry properties.

Findings

Centrifugal force changes sign at embedding diagram turning points.

Limits of embeddability are established for Kerr-Newman spacetimes.

Spacetimes are classified by the number of embeddable regions and turning points.

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. 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.