Concept of radius of gyration in general relativity

The radius of gyration is a familiar concept in Newtonian mechanics and a suitably defined relativistic generalization of it turns out to be very useful for analyzing rotational effects in strong gravitational fields. The present paper contains a discussion of the properties of this quantity and of its level surfaces (the von Zeipel cylinders) and also of its connection with the effective potential for photon motion and with ideas of centrifugal force. The direction of increase of the radius of gyration gives a preferred determination of the local outward direction relevant for the dynamical effects of rotation, but this direction becomes misaligned with the global outward direction in strong-field situations. This misalignment underlies some apparently counterintuitive behavior of the centrifugal force in strong fields which has recently been the subject of considerable interest.