The above cartoon depicts affect of the speed of light on unequal mass binary BH's. Essentially there may be no effect because M0 is very much greater than M1 so M1 orbits M0. Since M0 does not move (appreciably), gravity waves emanated by M0 arrive at M1 perpendicular to the motion of M1 which means M1 velocity is not affected by gravity propagation delay.
The above cartoon for Equal mass BH pairs shows that gravity propagated by each mass on the other arrives non-orthogonal which causes the gravity force to accelerate the opposing mass inward and causes it to move to a lower orbit??? This action does not violate conservation of energy; the lower orbit constitutes reduction in potential energy manifest in additional kinetic energy.
The above derived equation allows solving for the arrival time of a gravity wave at the opposing mass partner of an equal-mass Binary BH pair. A chart will be included that shows the angle traveled by the pair of masses versus the distance between the two singularities (expressed in multiples of Schwarzschild radius). Data for Rs*200 to Rs*0.1 yielded delayed action angles of 2.86 degrees to 128.07 degrees for a 10 Solar mass BH pair.
This non-orthogonal gravity wave arrival effect may be the reason that it is said that mass entering the event horizon is doomed to hit the singularity. But I don't think so because the effect does not exist for M0>>M1 Binaries. This result may suggest that it is very much less likely to find equal or nearly equal mass Binary BH's since they would tend to deorbit into each other. And conservation of angular momentum makes the end result of this scenario virtually unimaginable; talk about major gravity 'frame dragging'... Will run more numbers... Ran the numbers, below.
See, here is a problem; the radial force component of gravity toward CG is reduced by Cos(theta) and the tangential component goes to Fg times Sin(theta). The tangential component will speed up (M1) as expected but the reduced radial component would cause trajectory to heighten which would seem to violate conservation of energy.The above chart shows how far the angle to M0 (and by symmetry, M1) have progressed past t=0 following the mutual launch of gravity waves where the masses are located at 180 and zero degrees, respectively. Notice the closer the orbiting singularities are to the binary CG, the further they have traveled around the circular trajectory.
Why don't orbits of electrons about the nucleus decay? Need to run some angle numbers on that. The electrons are bound to the nucleus by the electrostatic force which propagates at c. What happens when an atom is cooled to absolute zero?, does the electron stop orbiting and fall into the nucleus? We will not even bring up the problems incurred by the quantum mechanical probability>zero of an electron belonging to that atom being at infinity.
Sure hope you enjoy this as much as I! More physicsstuff on this topic coming soon. dac