A first-order secular theory for the post-Newtonian two-body problem with spin – II. A complete solution for the angular coordinates in the restricted case

We adopt the Dirac–Detweiler–Whiting radiative and regular effective field in curved spacetime. Thereby, we derive straightforwardly the first order perturbative correction to the geodesic of the background in a covariant form, for the extreme mass ratio two-body problem. The correction contains the self-force contribution and a background metric-dependent term.

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Krein Stability in the Disturbed Two-Body Problem

Symposium - International Astronomical Union ◽

10.1017/s0074180900091403 ◽

1992 ◽

Vol 152 ◽

pp. 369-374

Author(s):

R. R. Cordeiro ◽

R. Vieira Martins

Keyword(s):

Small Parameter ◽

Integrable Systems ◽

Body Problem ◽

Major Axis ◽

Semi Major Axis ◽

First Order ◽

Two Body Problem

We present a method for the study of the Krein signature in perturbed Hamiltonian integrable systems. The method is developed up to first order in the small parameter. We apply this method to a particular instance of the two-body problem in which the semi-major axis is not affected by the perturbation.

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The perturbed three-dimensional two body problem: regular quaternion equations of relative motion

Прикладная математика и механика ◽

10.31857/s003282350002736-9 ◽

2018 ◽

Vol 82 (6) ◽

pp. 721-733

Author(s):

Yu. Chelnokov ◽

Keyword(s):

Relative Motion ◽

Body Problem ◽

Three Dimensional ◽

Two Body Problem

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The post-Newtonian approximation

10.1093/oso/9780198786399.003.0052 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

General Relativity ◽

Gravitational Field ◽

Body Problem ◽

Equations Of Motion ◽

Two Body Problem ◽

Newtonian Approximation ◽

Actual Motion ◽

Law Of Attraction ◽

Universal Law ◽

Two Bodies

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

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The two-body problem: an effective-one-body approach

10.1093/oso/9780198786399.003.0056 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Body Problem ◽

Equations Of Motion ◽

Reaction Force ◽

Kerr Black Hole ◽

Radiation Reaction ◽

Spherically Symmetric ◽

Geodesic Motion ◽

Two Body Problem ◽

Symmetric Spacetime ◽

Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

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