The generalized Jacobi equation

摘要: The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. linearization ignores relative velocity of geodesics. generalized takes into account; that is, when geodesics are neighbouring but their is arbitrary corresponding deviation equation. Hamiltonian structure this nonlinear analysed paper. tidal accelerations for test particles field a plane gravitational wave and exterior rotating mass investigated. In latter case, existence an attractor uniform radial motion with speed 2−1/2c ≈ 0.7c pointed out. astrophysical implication result terminal relativistic jet briefly explored.