Optical reference geometry and inertial forces in Kerr-de Sitter spacetimes
arXiv:gr-qc/0701028 · doi:10.1088/0264-9381/24/3/004
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.
31 pages, 10 figures
References in corpus (9)
- Influence of the relict cosmological constant on accretion discs
- Equatorial circular orbits in the Kerr-de Sitter spacetimes
- Equilibrium conditions of spinning test particles in Kerr-de Sitter spacetimes
- Optical reference geometry of the Kerr-Newman spacetimes
- Photon capture cones and embedding diagrams of the Ernst spacetime
- Gyroscopic Precession and Inertial Forces in Axially Symmetric Stationary Spacetimes
- Centrifugal force in Kerr geometry
- Inertial forces and the foundations of optical geometry
- Forces in Kerr spacetimes with a repulsive cosmological constant
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