ar X iv : g r - qc / 0 60 20 71 v 1 1 9 Fe b 20 06 Tidal Dynamics in Kerr Spacetime

The motion of free nearby test particles relative to a stable equatorial circular geodesic orbit about a Kerr source is investigated. It is shown that the nonlinear generalized Jacobi equation can be transformed in this case to an autonomous form. Tidal dynamics beyond the critical speed c/ √ 2 is studied. We show, in particular, that a free test particle vertically launched from the circular orbit parallel or antiparallel to the Kerr rotation axis is tidally accelerated if its initial relative speed exceeds c/ √ 2. Possible applications of our results to high-energy astrophysics are briefly mentioned.