Epicycles and Poincaré Resonances in General Relativity

Abstract

The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this note we point out some subtleties in the application of the method related to secular motions, in first as well as in higher order. In particular we work out the general second-order contribution to bound orbits in Schwarzschild space-time and show that it provides very good analytical results all the way up to the innermost stable circular orbit.

arXiv comment24 pages, 4 figures

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Cited by in corpus (7)

• Geodesic deviation at higher orders via covariant bitensors
• Spinning bodies in curved space-time
• Geodesic deviations: modeling extreme mass-ratio systems and their gravitational waves
• Ballistic orbits in Schwarzschild space-time and gravitational waves from EMR binary mergers
• On the Applicability of the Geodesic Deviation Equation in General Relativity
• Geodesic deviation to all orders via a tangent bundle formalism
• Spin-induced motion in black hole spacetime