Local and global gravitomagnetic effects in Kerr spacetime

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Abstract
The integral shift in orientation of a gyroscope in closed polar orbit in the Kerr spacetime is examined as an example of a global gravitomagnetic effect. The exact dependence of this effect on the mass and angular momentum parameters of the Kerr field is determined and the well-known weak-field slow-motion limit pertinent to forthcoming experiments is analyzed. The precession of the spin vector of a gyroscope stationed at a given point of the Kerr spacetime’s symmetry axis is presented as a local counterpart of the above gravitomagnetic effect.