REDUCTION OF THE TWO-BODY PROBLEM WITH SPIN IN (2+1)-DIMENSIONAL GRAVITY

The two-body problem with spin in (2+1)-dimensional gravity is analyzed nonperturbatively. Utilizing topological methods similar to those used in the reduction of the spinless case, we show that the general two-body problem with spin can again be reduced to an equivalent one-body formalism. We give exact expressions for the mass and spin of the reduced problem.

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NON-PERTURBATIVE GAUGE THEORETIC TREATMENT OF TWO-PARTICLE SCATTERING IN (2 + 1)-DIMENSIONAL GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732392001920 ◽

1992 ◽

Vol 07 (24) ◽

pp. 2173-2178 ◽

Cited By ~ 3

Author(s):

M. K. FALBO-KENKEL ◽

F. MANSOURI

Keyword(s):

Phase Space ◽

Body Problem ◽

Equal Mass ◽

Suitable Choice ◽

Particle Scattering ◽

Two Body Problem ◽

Relative Coordinate ◽

Deficit Angle ◽

Dimensional Gravity ◽

Chern Simons

By a suitable choice of phase space variables, which is natural for the reduction of a two-body problem, we couple two sources to the Chern-Simons-Witten action and obtain the exact two-body Hamiltonian. For particles of (nearly) equal mass and of small momenta, the Hamiltonian reduces to that of 't Hooft. In the corresponding geometry, when viewed from a particular frame, the relative coordinate moves on a cone of deficit angle equal to the classical Hamiltonian.

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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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