  We point out novel consequences of general relativity involving tidal
dynamics of ultrarelativistic relative motion. Specifically, we use the
generalized Jacobi equation and its extension to study the force-free dynamics
of relativistic flows near a massive rotating source. We show that along the
rotation axis of the gravitational source, relativistic tidal effects strongly
decelerate an initially ultrarelativistic flow with respect to the ambient
medium, contrary to Newtonian expectations. Moreover, an initially
ultrarelativistic flow perpendicular to the axis of rotation is strongly
accelerated by the relativistic tidal forces. The astrophysical implications of
these results for jets and ultrahigh energy cosmic rays are briefly mentioned.
