scholarly journals Fixation of Physical Space-Time Coordinates and Equation of Motion of Two-Body Problem

1961 ◽  
Vol 26 (2) ◽  
pp. 157-172 ◽  
Author(s):  
Toshiei Kimura
Keyword(s):  
Body Problem ◽  
Physical Space ◽  
Equation Of Motion ◽  
Space Time ◽  
Two Body Problem

The static two body problem

1974 ◽  
Vol 75 (2) ◽  
pp. 249-260 ◽  
Author(s):  
H. Müller Zum Hagen
Keyword(s):  
Perfect Fluid ◽  
Physical Meaning ◽  
Body Problem ◽  
Space Time ◽  
Equilibrium Conditions ◽  
Two Body Problem ◽  
Special Cases ◽  
Static Solutions ◽  
Two Bodies ◽  
Extended Bodies

AbstractThe problem of whether there exist static solutions of Einstein's equations for two extended bodies surrounded by vacuum is investigated. Equilibrium conditions for the general static situation are derived and their physical meaning discussed. Special cases of the problem are solved by using these equilibrium conditions. In one of these cases, the essential assumptions are that the space time is axisymmetric and that the matter of which the two bodies are composed consists of perfect fluid. Solu tions are also obtained in which these restrictions are weakened.

The post-Newtonian approximation

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.

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

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.

A Fitted Runge-Kutta-Nyström Method with Six Stages for the Integration of the Two-Body Problem

2011 ◽  
Author(s):  
A. A. Kosti ◽  
Z. A. Anastassi ◽  
T. E. Simos ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Body Problem ◽  
Two Body Problem ◽  
Runge Kutta

Analytic solutions of the two-body problem with variable mass

Icarus ◽  
1966 ◽  
Vol 5 (1-6) ◽  
pp. 34-46 ◽  
Author(s):  
John D. Hadjidemetriou
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Analytic Solutions ◽  
Two Body Problem

Axially symmetric gravitational two-body problem of Cooperstock, Lim, and Hobill

1982 ◽  
Vol 25 (12) ◽  
pp. 3433-3437 ◽  
Author(s):  
Martin Walker ◽  
Clifford M. Will
Keyword(s):  
Body Problem ◽  
Axially Symmetric ◽  
Two Body Problem

scholarly journals Non-Collision Singularities in the Planar Two-Center-Two-Body Problem

2016 ◽  
Vol 345 (3) ◽  
pp. 797-879 ◽  
Author(s):  
Jinxin Xue ◽  
Dmitry Dolgopyat
Keyword(s):  
Body Problem ◽  
Two Body Problem
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