**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;