**Publication date:** Jun 2006

**Abstract:**

Equilibrium conditions and spin dynamics of spinning test particles are

discussed in the stationary and axially symmetric Kerr de Sitter

black-hole or naked-singularity spacetimes. The general equilibrium

conditions are established, but due to their great complexity, the

detailed discussion of the equilibrium conditions and spin dynamics is

presented only in the simple and most relevant cases of equilibrium

positions in the equatorial plane and on the symmetry axis of the

spacetimes. It is shown that due to the combined effect of the rotation

of the source and the cosmic repulsion the equilibrium is spin dependent

in contrast to the spherically symmetric spacetimes. In the equatorial

plane, it is possible at the so-called static radius, where the

gravitational attraction is balanced by the cosmic repulsion, for the

spinless particles as well as for spinning particles with arbitrarily

large phiv-oriented spin or at any radius outside the ergosphere with a

specifically given spin orthogonal to the equatorial plane. On the

symmetry axis, the equilibrium is possible at any radius in the

stationary region and is given by an appropriately tuned spin directed

along the axis. At the static radii on the axis the spin of particles in

equilibrium must vanish.

**Authors:**

Stuchlík, Zdenek; Kovár, Jirí;