Optical reference geometry of the Kerr-Newman spacetimes

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.

28 pages, 17 figures

References in corpus (3)

• The Many Faces of Gravitoelectromagnetism
• Photon capture cones and embedding diagrams of the Ernst spacetime
• Centrifugal force in Kerr geometry

Cited by in corpus (14)

• Off-equatorial orbits in strong gravitational fields near compact objects -- II: halo motion around magnetic compact stars and magnetized black holes
• Equatorial circular orbits of neutral test particles in the Kerr--Newman spacetime
• Quasiperiodic Oscillations, Quasinormal Modes and Shadows of Bardeen-Kiselev Black Holes
• General relativistic polytropes with a repulsive cosmological constant
• Off-equatorial orbits in strong gravitational fields near compact objects
• Polytropic spheres containing regions of trapped null geodesics
• A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole
• Optical reference geometry and inertial forces in Kerr-de Sitter spacetimes
• Neutrino trapping in braneworld extremely compact stars
• Fermion self-trapping in the optical geometry of Einstein-Dirac solitons
• Hořava's quantum gravity illustrated by embedding diagrams of the Kehagias-Sfetsos spacetimes
• Forces in Kerr spacetimes with a repulsive cosmological constant
• Embedding diagrams in stationary spacetimes
• Charged fluids encircling compact objects: force representations and conformal geometries