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Geodesic deviations: modeling extreme mass-ratio systems and their gravitational waves
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The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild space-time. The results are used to construct analytic expressions for the source terms in the Regge-Wheeler and Zerilli-Moncrief equations, which describe the propagation of gravitational waves emitted by a compact massive object moving in the Schwarzschild background space-time. The wave equations are solved numerically to provide the asymptotic form of the wave at large distances for a series of non-circular bound orbits with periastron distances up to the ISCO radius, and the power emitted in gravitational waves by the extreme-mass ratio binary system is computed. The results compare well with those of purely numerical approaches.
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Geodesic deviation to all orders via a tangent bundle formalism
A tangent-bundle flow formalism yields an explicit all-orders formula for the Jacobi propagators in geodesic deviation, with the Lagrangian and equation of motion given explicitly up to tenth order.
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