Some aspects of motion in the Kerr field

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We find that the Kerr field, the simplest relativistic gravitational field of a rotating source, may help in (pre-)collimation of cosmic jets emanating from many active galactic nuclei. Solving the geodesic motion in the Kerr field, we use in part a tetrad approach — the description of quantities by their physically measured components in the locally Cartesian frame of a local observer (rather than by their coordinate components). The stationary frames, the most important local frames in the Kerr spacetime, are reviewed and their properties discussed. We use the Newtonian “force” language to interpret the occurrence of the “rotospheres”, the toroidal regions that circle round the Kerr sources; in these regions, the 4-acceleration of a stationary observer depends on his orbital angular velocity in a way going against common intuition. We give the rotospheres in various Kerr spacetimes and introduce a new class of privileged observers (“extremally accelerated observers”). We then generalize this approach to any motion in any spacetime. In the Kerr spaces, we construct the cones generated by directions along which photons can escape to infinity from a given point. The results are consistent with the expected influence of rotational dragging for black holes, whereas they are rather complicated for naked singularities.