I have a 10-year-old cousin who is very curious about the world, and physics in particular. When his mother sent me two very interesting questions that he asked about black holes, I had fun coming up with some answers for him. His questions and my answers are reproduced below. (Yes, some of the language isn’t quite as precise as it should be, but I intentionally glossed over a few details. Hopefully I didn’t say anything wrong as a result.)
If a black hole “sucked in” only photons, would it increase in mass?
Photons “die” when they interact with something, but if they do die, then what are they interacting with in the black hole?
These are two great questions, and I had fun coming up with answers to them. I gave a short answer, but any good physics question brings up a lot of related ideas, so I also put a longer answer that brings up some other ideas.
Yes. Einstein taught us that energy and mass are two aspects of the same thing. Even though the photons are massless on their own, their energy can increase the mass of the black hole when they are absorbed. The event horizon prevents any information from escaping a black hole, so we can’t know exactly what the photon interacts with.
When a photon is absorbed by regular matter (anything you see around you), its energy is absorbed by by one of the particles in that object. For example, an electron absorbs the photon, and moves to a higher energy state within the atom. The key thing to remember is that there are billions and billions of different ways the photon can be absorbed by regular matter.
Black holes are much simpler. They have only 3 things that we can know about them: their mass, their electric charge, and how fast they are rotating. Physicists say that black holes have “no hair” to say that there are no other details that we can know about them.
So if we are sitting outside a black hole, and a photon falls past the horizon of the black hole, we can see how much it increased the mass or rotation of the black hole. Either way, the energy of the photon has now been added to the energy of the black hole. (See note below)
Now, why can’t we know what happens to the photon once it’s inside the black hole? Anything inside the event horizon can never come back out — that’s why we call them black holes. So we can’t do an experiment to see what happens, because we’d never see the results! Another problem is that the photon’s behavior is explained by quantum mechanics, and the black hole is explained by general relativity. No one knows how to make these two theories work together, so we can’t make a prediction that would involve both theories. String theory is one idea to solve problems like these, but it doesn’t work yet.
An outside observer can’t actually “watch” anything pass the horizon of the black hole. The outside observer will perceive the infalling matter as infinitely red-shifted, and taking an infinite amount of time to reach the horizon. However, the object falling into the black hole will cross the horizon in a finite amount of its “own” time.
Now, a question of my own, for anyone who knows more GR than I do: does this mean that an outside observer will never be able to observe a mass increase for the black hole?