**Publication date:** Feb 2007

**Abstract:**

Optical reference geometry and the 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 wholly cover the stationary regions of the spacetimes, therefore the

limits of embeddability are established. The 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.

**Authors:**

Kovář, Jiří; Stuchlík, Zdenek;