scholarly journals The gravitational two-body problem in the vicinity of the light ring: Insights from the black-hole–ring toy model

2013 ◽  
Vol 726 (1-3) ◽  
pp. 533-536 ◽  
Author(s):  
Shahar Hod
Keyword(s):  
Black Hole ◽  
Body Problem ◽  
Two Body Problem ◽  
Light Ring

scholarly journals Binary collisions in popovici’s photogravitational model

2002 ◽  
pp. 9-16 ◽  
Author(s):  
V. Mioc ◽  
C. Blaga
Keyword(s):  
Black Hole ◽  
Body Problem ◽  
Equations Of Motion ◽  
Gravitational Attraction ◽  
Two Body Problem ◽  
Binary Collisions ◽  
Combined Action ◽  
Collision Manifold ◽  
S Model ◽  
Hole Effect

The dynamics of bodies under the combined action of the gravitational attraction and the radiative repelling force has large and deep implications in astronomy. In the 1920s, the Romanian astronomer Constantin Popovici proposed a modified photogravitational law (considered by other scientists too). This paper deals with the collisions of the two-body problem associated with Popovici?s model. Resorting to McGehee-type transformations of the second kind, we obtain regular equations of motion and define the collision manifold. The flow on this boundary manifold is wholly described. This allows to point out some important qualitative features of the collisional motion: existence of the black-hole effect, gradientlikeness of the flow on the collision manifold, regularizability of collisions under certain conditions. Some questions, coming from the comparison of Levi-Civita?s regularizing transformations and McGehee?s ones, are formulated.

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

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
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