Question: I would like to know what would show that a black hole
was moving farther away from you? My specific wonders would be how light around the hole would act, how its shape would change, or if the black hole would start to reflect less and less light? – Billy
Answer: Remember that you cannot really “see” a black hole. All you really see is stuff being gobbled-up by the black hole, which emit very high energy light just as they are being sucked into the black hole. So, if you noticed that the high energy light that is emitted by these objects was getting “redder”, or being emitted at a longer and longer wavelength, that would be a sign that the black hole was moving at a more rapid pace away from you. If a black hole is embedded within an environment where its supply of matter was decreasing, then you would see less and less high energy light coming from the region around the black hole as this supply dwindled. There is a nice description of what a black hole looks like (with pictures!) on the Universe Today description regarding just this question.