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.
Highlights
Because a Living Reviews article can evolve over time, we recommend to cite the article as follows: Toshifumi Futamase and Yousuke Itoh, “The Post-Newtonian Approximation for Relativistic Compact Binaries”, Living Rev
Using the so-obtained RA-independent field, we evaluate the surface integrals in the general form of the 3 PN equations of motion by discarding the RA dependence emerging from the surface integrals, and obtain the equations of motion
The surface integral approach is achieved by using the local conservation of the energy momentum, which led us to the general form of the equations of motion that are expressed entirely in terms of surface integrals
Summary
The motion and associated emission of gravitational waves (GW) of self-gravitating systems have been a main research interest in general relativity. The most systematic among those works that have succeeded in achieving higher order iteration are the ones by Blanchet, Damour, and Iyer who have developed a scheme to calculate the waveform at a higher order, where the post-Minkowskian approximation is used to construct the external field and the post-Newtonian approximation is used to construct the field near the material source They and their collaborators have obtained the waveform up to 3.5 PN order which is of order 7 higher than the lowest quadrupole wave [23, 24, 29, 31, 32] by using the equations of motion up to that order [22, 91, 93, 111, 123, 130].
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