Gravitomagnetic Accelerators

We study a simple class of time-dependent rotating Ricci-flat cylindrically symmetric spacetime manifolds whose geodesics admit gravitomagnetic jets. The helical paths of free test particles in these jets up and down parallel to the rotation axis are analogous to those of charged particles in a magnetic field. The jets are attractors. The jet speed asymptotically approaches the speed of light. In effect, such source-free spacetime regions act as "gravitomagnetic accelerators".Comment: 4 pages, 2 figures; v2: reference added; v3: slightly expanded version accepted for publication in Phys. Lett.

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/sqrt(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/sqrt(2). Possible applications of our results to high-energy astrophysics are briefly mentioned.Comment: 15 pages, 3 figures; v2: slightly expanded version accepted for publication in CQ

On the Ionization of a Keplerian Binary System by Periodic Gravitational Radiation

The gravitational ionization of a Keplerian binary system via normally incident periodic gravitational radiation of definite helicity is discussed. The periodic orbits of the planar tidal equation are investigated on the basis of degenerate continuation theory. The relevance of the Kolmogorov-Arnold-Moser theory to the question of gravitational ionization is elucidated, and it is conjectured that the process of ionization is closely related to the Arnold diffusion of the perturbed system.Comment: 19 pages, REVTEX Style, To appear in JM

Ultrarelativistic Motion: Inertial and Tidal Effects in Fermi Coordinates

Fermi coordinates are the natural generalization of inertial Cartesian coordinates to accelerated systems and gravitational fields. We study the motion of ultrarelativistic particles and light rays in Fermi coordinates and investigate inertial and tidal effects beyond the critical speed c/sqrt(2). In particular, we discuss the black-hole tidal acceleration mechanism for ultrarelativistic particles in connection with a possible origin for high-energy cosmic rays.Comment: 13 pages, 3 figures, slightly expanded version accepted for publication in Class. Quantum Gra

Tidal effects on magnetic gyration of a charged particle in Fermi coordinates

We examine the gyration motion of a charged particle, viewed from a reference observer falling along the Z axis into a Schwarzschild black hole. It is assumed that the magnetic field is constant and uniform along the Z axis, and that the particle has a circular orbit in the X-Y plane far from the gravitational source. When the particle as well as the reference observer approaches the black hole, its orbit is disrupted by the tidal force. The final plunging velocity increases in the non-relativistic case, but decreases if the initial circular velocity exceeds a critical value, which is approximately 0.7c. This toy model suggests that disruption of a rapidly rotating star due to a velocity-dependent tidal force may be quite different from that of a non-relativistic star. The model also suggested that collapse of the orbit after the disruption is slow in general, so that the particle subsequently escapes outside the valid Fermi coordinates.Comment: 10 pages, 12 figure

Chaos in the Kepler System

The long-term dynamical evolution of a Keplerian binary orbit due to the emission and absorption of gravitational radiation is investigated. This work extends our previous results on transient chaos in the planar case to the three dimensional Kepler system. Specifically, we consider the nonlinear evolution of the relative orbit due to gravitational radiation damping as well as external gravitational radiation that is obliquely incident on the initial orbital plane. The variation of orbital inclination, especially during resonance capture, turns out to be very sensitive to the initial conditions. Moreover, we discuss the novel phenomenon of chaotic transition.Comment: RevTeX, 22 pages, 6 figure

Invariant tori for periodically perturbed oscillators

The response of an oscillator to a small amplitude periodic excitation is discussed. In particular, sufficient conditions are formulated for the perturbed oscillator to have an invariant torus in the phase cylinder. When such an invariant torus exists, some perturbed solutions are in the basin of attraction of this torus and are thus entrained to the dynamical behavior of the perturbed system on the torus. In particular, the perturbed solutions in the basin of attraction of the invariant torus are entrained to a subharmonic or to a quasi periodic motion