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Review
. 2007;10(1):2.
doi: 10.12942/lrr-2007-2. Epub 2007 Mar 12.

The Post-Newtonian Approximation for Relativistic Compact Binaries

Toshifumi Futamase  1 , Yousuke Itoh  1
Affiliations
Review

The Post-Newtonian Approximation for Relativistic Compact Binaries

Toshifumi Futamase et al. Living Rev Relativ. 2007.

Abstract

We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive post-Newtonian equations of motion for relativistic compact binaries based on a surface integral approach and the strong field point particle limit. As an application we derive third post-Newtonian equations of motion for relativistic compact binaries which respect the Lorentz invariance in the post-Newtonian perturbative sense, admit a conserved energy, and are free from any ambiguity.

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Figures

Figure 1
Figure 1
Body zone coordinates and near zone coordinates. In the near zone coordinates (τ, xi), both the body zone and the star shrink as ϵ (thin dotted arrow) and ϵ2 (thick dotted arrow) respectively. Both the thin and thick arrows point inside. In the body zone coordinates formula image, the star does not shrink while the body zone boundary goes to infinity as ϵ−1 (thin dotted line pointing outside).
Figure 2
Figure 2
Gravitational energy momentum flux through the body zone boundary. The meshed two circles represent stars 1 and 2. Each star is surrounded by the body zone represented here by a striped area. The arrows around star 1 represent the gravitational energy momentum flux flowing through the body zone boundary.
Figure 3
Figure 3
The vectors used in the surface integral over the boundary of the body zone 1.
Figure 4
Figure 4
Flowchart of the post-Newtonian iteration.
See this image and copyright information in PMC

References

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