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If we imagine that the object is a large bowling ball, held in the hands of an astronaut we can imagine an experiment that she may conduct. While approaching the event horizon, the astronaut is brought to a halt and she then applies a force to the ball, the ball accelerates and moves from one hand to the other. The force would be a set quantity and known to both her and an observer far away. By doing this experiment the astronaut can determine the mass of the ball by observing the acceleration between her hands. The outside observer can see the experiment unfold at a distance and also measure the acceleration, therefore determining a mass.

I am curious; from the point of view of the astronaut I expect she measures the same mass for the ball that was determined while she was far away with the other observer before being lowered into the BH. The distant observer, however, is able to recover the rest mass of the bowling ball as usable energy. Once the ball is dropped into the BH, he measures no change in the mass of the BH. What results would the distant observer measure while watching the astronaut’s experiment from far away? Would he see the astronaut successfully measure a mass for the ball and how would he explain anything that he is a witness to?