Optical reference geometry and inertial forces in Kerr-de Sitter spacetimes

TL;DR

This paper explores the optical reference geometry and inertial forces in Kerr-de Sitter spacetimes, illustrating their properties, behavior, and implications for particle motion and spacetime classification.

Contribution

It provides a detailed analysis of inertial forces and optical geometry in Kerr-de Sitter spacetimes, including embedding diagrams and classification based on inertial force properties.

Findings

Inertial forces exhibit characteristic behaviors in Kerr-de Sitter spacetimes.

Embedding diagrams reveal limits of embeddability and relate to centrifugal force behavior.

Spacetimes are classified according to inertial force and embedding diagram properties.

Abstract

Optical reference geometry and related concept of inertial forces are investigated in Kerr-de Sitter spacetimes. Properties of the inertial forces are summarized and their typical behaviour is illustrated. The intuitive 'Newtonian' application of the forces in the relativistic dynamics is demonstrated in the case of the test particle circular motion, static equilibrium positions and perfect fluid toroidal configurations. Features of the optical geometry are illustrated by the embedding diagrams of its equatorial plane. The embedding diagrams do not cover whole the stationary regions of the spacetimes, therefore the limits of embeddability are established. A shape of the embedding diagrams is related to the behaviour of the centrifugal force and it is characterized by the number of turning points of the diagrams. Discussion of the number of embeddable photon circular orbits is also included and the typical embedding diagrams are constructed. The Kerr-de Sitter spacetimes are classified according to the properties of the inertial forces and embedding diagrams.