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Is there a retarded potential concept in gravitational field similar to electromagnetic radiation?

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dear user26742 have you seen… and the answers there? If so, maybe you could ask what else you want to know about gravity radiation further to the pithy descriptions in the answers on that web page. – WetSavannaAnimal aka Rod Vance Aug 3 '13 at 9:14

The concept of a retarded potential presupposes that we can fix some inertial frame, and in that frame there is a uniquely defined time coordinate, which we can use to measure the retardation. All of this fails in GR. GR doesn't have global frames of reference. Any time coordinate can be changed by feeding it through a smooth, one-to-one function, and output of the this change of coordinates is still a valid time coordinate.

In electromagnetism, we have a four-potential $A$, and differentiation of this potential gives the observable fields. The best analogy in GR is that we have the metric $g$, and a second derivative of this gives the Riemann tensor, which is what's observable. So $g$ can be thought of as "the potential." (In a static spacetime $g$ can be written in terms of a scalar potential $\Phi$, but that's of no interest here because we're talking about gravitational waves, so the spacetime isn't static.) The question is then whether we can have a "retarded metric." For the reasons given in the first paragraph, the answer is in general no. However, in the limit of weak fields, the answer is yes. For a treatment in this style, see Carroll, Lecture Notes on General Relativity, ch. 6.

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@user26724 note that what Ben says does not tell against what the web link I gave said. Both the answers given there were dealing with what they called "post Newtonian formalism" - which is essentially the Carroll lectures approach for a weak field given in Ben's answer. I might be wrong here, but I seem to see different authors calling slightly different things "post Newtonian formalism" - another name for the treatment in Ben's link is "Linear Einstein Equations" or "Weak Field Einstein Equations" (cf also Section 8.3, Bernard Schutz "A First Course in General Relativity".) – WetSavannaAnimal aka Rod Vance Aug 4 '13 at 6:02

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