If 2 masses are moving apart or towards each other, does the force of gravity between them vary relativistically? If a gravitational field propagates at C, and a mass originating the field is moving relative to another mass, then is a Lorentz factor needed to describe their gravitational interaction?
That is:
The Force of attraction given by the simple Newtonian equation:
Can be rewritten by substituting:
If this is mathematically correct, then 2 objects moving away from each other at velocity greater than C should experience repulsive (or anti) gravity, and in a galaxy where there are many mass pairs where v2/c2 is non-trivial, there will be stronger than expected gravitational attraction.
Can the cumulative gravitational force on an object be approximated by the sum of pairwise forces of relativistic gravity where each pairwise force is a function of the relative velocity between masses?
