FORCES IN KERR SPACE–TIMES WITH A REPULSIVE COSMOLOGICAL CONSTANT

Abstract

Forces defined in the framework of optical reference geometry are introduced in the case of stationary and axially symmetric Kerr black hole and naked-singularity space–times with a repulsive cosmological constant. Properties of the forces acting on test particles moving along circular orbits in the equatorial plane are discussed, whereas it is shown where the gravitational force vanishes and changes its orientation and where the centrifugal force vanishes and changes its orientation independently of the velocity of test particles related to the optical geometry; the Coriolis force does not vanish for the velocity being nonzero. The space–times are classified according to the number of circular orbits where the gravitational and centrifugal forces vanish.