Spin-geodesic deviations in the Schwarzschild spacetime

Abstract

The deviation of the path of a spinning particle from a circular geodesic in the Schwarzschild spacetime is studied by an extension of the idea of geodesic deviation. Within the Mathisson-Papapetrou-Dixon model and assuming the spin parameter to be sufficiently small so that it makes sense to linearize the equations of motion in the spin variables as well as in the geodesic deviation, the spin-curvature force adds an additional driving term to the second order system of linear ordinary differential equations satisfied by nearby geodesics. Choosing initial conditions for geodesic motion leads to solutions for which the deviations are entirely due to the spin-curvature force, and one finds that the spinning particle position for a given fixed total spin oscillates roughly within an ellipse in the plane perpendicular to the motion, while the azimuthal motion undergoes similar oscillations plus an additional secular drift which varies with spin orientation.

16 pages, 3 figures; published version

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Cited by in corpus (21)

• Hamilton-Jacobi equation for spinning particles near black holes
• Gyroscopes orbiting black holes: A frequency-domain approach to precession and spin-curvature coupling for spinning bodies on generic Kerr orbits
• Covariant hamiltonian spin dynamics in curved space-time
• Deviation of quadrupolar bodies from geodesic motion in a Kerr spacetime
• Spinning massive test particles in cosmological and general static spherically symmetric spacetimes
• Spin-geodesic deviations in the Kerr spacetime
• Spinning bodies in curved space-time
• Dynamics of quadrupolar bodies in a Schwarzschild spacetime
• Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism
• Generalized deviation equation and determination of the curvature in General Relativity
• Extended bodies in a Kerr spacetime: exploring the role of a general quadrupole tensor
• Spinning particle orbits around a black hole in an expanding background
• Detweiler's redshift invariant for spinning particles along circular orbits on a Schwarzschild background
• Hyperbolic-like elastic scattering of spinning particles by a Schwarzschild black hole
• Gyroscope precession along unbound equatorial plane orbits around a Kerr black hole
• Symplectic mechanics of relativistic spinning compact bodies II.: Canonical formalism in the Schwarzschild spacetime
• Effect of an arbitrary spin orientation on the quadrupolar structure of an extended body in a Schwarzschild spacetime
• Observer-dependent tidal indicators in the Kerr spacetime
• Precisely computing bound orbits of spinning bodies around black holes I: General framework and results for nearly equatorial orbits
• Interpreting gravitational fields of Topologically Massive Gravity using geodesic deviation
• Precisely computing bound orbits of spinning bodies around black holes II: Generic orbits