Gary,
Glad to see you looking in. I think among the three of us we agree that gravitation to be realistically defined as a physical phenomenon, must be addressed in non-linear fashion. I personally go from an exponential 'stacking up', or 'deceleration', of energy into a self-gravitational spherical free rest mass. But that's not where Ed is coming from and I'm simply looking for a fit.
I agree with Ed that 1/r^2 is insufficient. It can be treated as a near approximation in a straight line measurement that operates as a time independent invariance theorem similar in form to the time derivative invariance of the LT.
Pardon the "A" in my previous post, I'm really bad about things like that. Poor discipline, and besides, who decided to denote "B" as the magnetic plane? I always think "F" for 'ferrous'. But that needs reserved for 'force'. I'm okay with "E" for the electrostatic, and elasticity. We just don't have enough glyphs to go around. Oh well.
I can vaguely discern in your waveform suggestion that the cosine of theta would produce an amplitude, I am not trained mathematically to readily see things like that. And its each to their own, and if two different methods define the same process then its corroborative. Ed has a function he says he has yet to chart, but one must assume that its derivative of his global scheme of things in equating gravitational behavior with time dependent energy density.
I personally think, an R4 model of EMR that is self-limiting to observed limits, and which would be directly transformative to to S3 would be essential to bridging Relativity and QM. And think where we can look for a theoretical absolute velocity is in the core values of a free rest mass. I won't tout my own thing, it has legs but ticklish spots on both Achille's Heels. But I will say that where my modeling fails in part is that I have never gone back and put the EMR waveform in motion. Realistically, a soliton with a 'Pinch Point' that Ed colloquially (I'm good with colloquial!) describes, should race along at c like when you shake the bends out of your good extension cord after dragging it around for an hour. You know, you look at which way the kinks are winding and walk it out straightish and start giving it circular little whips, and the uncoil loop snakes down the length to where it hits a carbuncle, and unlays it.
Where I'm fuzzy about a gravitational mass interacting in a field of lower energy density, is not that the non-linearity in the mass would seek a greater field density to match its own density center, but rather how that non-linear field of lower density propagates from another gravitational mass among others in continually changing positions melding into the global system locale. That's got to be a lot of work. Good Cheer, jrc