Black holes are not necessarily static objects. It is possible for them to aquire mass as might happen if it was part of a binary "star" system. The black hole would then draw off part of the star's envelope of gases and form an accretion disk which spirals into the black hole. A black hole can also pick up gas from the interstellar medium which is what would happen if there was a gas cloud within its sphere of influence. If a black hole was part of a binary system, the rotation about the common center of gravity would cause the binary system to lose some energy in the form of gravity waves. The two stars would eventually spiral down into each other and coalesce. Some people think the gamma ray bursts are the result of the collision of two black holes.

Check out the note that I posted above regarding the motion of photons in a gravitational field. I don't feel comfortable with posting the solution on someone elses website, especially when the people who own the site claim ownership of what is posted. Posting the problem seemed like a good compromise. A college freshman or sophomore physics student would probably be able to follow the argument. I'll see what I can do to post my solution elsewhere. The problem was what motivated me to ask Bruce about light escaping from a black hole.

Jim