Retarded potential in gravitational field? Is there a retarded potential concept in gravitational field similar to electromagnetic radiation?
 A: 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.
