Suppose there is an object floating in space which over time begins to fall toward the source of a gravitational field. As it falls, its motion happens to be such that it gets locked in orbit around the source with a greater velocity than it had before it 'began to fall'. So it's gravitational potential has been converted to kinetic energy. According to relativity, this increased speed should increase the gravitational potential of the object (and therefore the object + the original source of the field), correct?
Does this mean that as a result of this, the expansion of the Universe should slow down slightly (because there is now a slightly greater gravitational potential in the Universe)? And if so, would that imply that the conversion from gravitational potential to kinetic energy is in a sense a conversion between the bulk kinetic energy of the expanding Universe and the local kinetic energy of a test mass?