Epicycles and Poincaré resonances in general relativity

G. Koekoek and J. W. van Holten
Phys. Rev. D 83, 064041 – Published 29 March 2011

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 paper we construct an improved parametrized version of the method, and discuss some subtleties in its application 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.

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  • Received 25 November 2010

DOI:https://doi.org/10.1103/PhysRevD.83.064041

© 2011 American Physical Society

Authors & Affiliations

G. Koekoek*

  • Physics Department, Vrije Universiteit, 1081 HV Amsterdam, Netherlands

J. W. van Holten

  • Nikhef, P.O. Box 41882 1009 DB Amsterdam, Netherlands

  • *gkoekoek@nikhef.nl
  • v.holten@nikhef.nl

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Vol. 83, Iss. 6 — 15 March 2011

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