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Yes it will. Or else these obects would be able to break light speed. Adding energy comes from where? A force acting on something over distance. Same thing is occuring.
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Could you get those objects to break light speed, using gravity, without them already being inside a black hole?
My knowledge of relativity is .. sketchy.
It just seems wrong that if you took two objects, and placed them in orbit around each other, the mass of the system could fluxuate without any outside energy input...