When black holes collide they do give off gravitational waves. When this happens, does it affect the information contained in the black holes? I can appeal to another one of these theorems that was proven by Stephen Hawking and friends, the area theorem of black holes. And then you let the black holes collide and they give off energy and gravitational waves, but they haven't shrunk overall. So if you think that the information is proportional to the event horizon area, it does not go down when you take two black holes and squeeze them together.