Suppose three objects are moving through space parallel to each other,. So, they're side by side horizontally, and all moving at the same speed, at some fraction of C. From a gravity perspective, wouldn't each object perceive the other two to be pulling on it from a direction slightly behind, because the of propagation delay? The last point at which a gravity wave would have been emitted in time to reach it was physically located a little behind where the objects are now.
And, if that were true, wouldn't the objects be constantly slowing down from each other's gravity? How does GR get around that?