So where do black holes fit in Special/General Relativity? Well, imagine you are on a ship just outside of the event horizon of a black hole, and you are traveling fast enough that you won't fall in (remember, you will be falling in, but if you are moving fast enough, you can fall around the curve of the black hole). Depending on how close you are, you are going to have to be moving really really fast. This means two things for you:
- You are in a big gravity well, so time is moving much slower for you than the rest of the universe that is not in a big gravity well.
- You are moving really fast, which also makes time run much slower for you than the rest of the universe that is not moving fast.
I hope you aren't planning on returning home to your family, because chances are great that they'll be dead a long time before you get back.
Now imagine you launch a probe into the black hole to study it (although once it crosses the event horizon, you'll never hear from it again, but let's suppose you are interested in the data up until that point). As you watch the probe go down to the black hole, you will notice it getting slower and slower. In fact, you will watch it and it will take a really really really long time.
Why? Because time for the probe is slowing down even more as it approaches the black hole. Your time moves along like normal (from your perspective), but the probe is accelerating in space but decelerating in time. How much depends on the size of the black hole.
Now let's talk about the event horizon, because this is where the not-so-black part comes in. The event horizon is not the surface of the black hole, if there is even such a thing (the problem is that our equations go haywire when we try to describe a black hole, where our laws of big things like planets meets the world of ultra-small things like atoms). It's only the point at which light no longer escapes.
In fact, you might not even know when you cross it. It's actually possible to cross the event horizon of a black hole and survive, assuming the black hole is large enough. You will be able to see what actually happens inside the black hole. If you could actually manage to get back out, you would win Nobel prizes and be famous. But you won't. Your fate was determined the moment you crossed the horizon.
Nothing comes out of a black hole. Physicists sometimes refer to this as information loss, because anything that falls in there will basicalaly be unobservable forever. There was some debate about whether information loss made sense, but there was debate about whether black holes actually exist. We know they do now. The proof? When black holes collide (yep, they sometimes pull each other together), they create a special kind of wave called a gravity wave.
Einstein predicted them, but it was really really hard to prove. It would take a cosmic event like two black holes colliding for us to even detect it. Eventually an experiment was designed to detect them. At multiple locations around the globe, detectors are installed, and they are isolated from all vibrations around them on the earth. The only way these detectors will detect anything is if a gravity wave passes through them. Of course, it would be impossible to be sure that they had eliminated even the strongest vibrations on earth, so that's why there are multiple ones.
If there was some vibration traveling through the earth - even an asteroid striking the earth - the detectors would detect that vibration at different times. Vibrations moving through the earth move really slowly, while gravity waves travel at the speed of light. Even if there was a difference in the timing of the detections, it would be really small. They installed the detectors and waited ... and waited ... and waited. It took a long time, but finally an event happened, and as predicted, the gravity waves were detected. Since then, more have been detected, and Einstein was proven right once again.