We now have a few working examples of a microscopic theory of quantum gravity, all come with specific boundary conditions (like any other equation in physics or mathematics), but otherwise full background independence. In particular, all those theories include quantum black holes, and we can ask all kinds of puzzling questions about those fascinating objects. Starting with, what is exactly a black hole?
In classical general relativity black hole is simply a fully collapsed star. This is a system where, in the end of its long evolution, gravity has become the dominant force, pushing matter into ever increasing density. Until, after some finite time, the matter becomes so dense that we lose our ability to describe the system using known physics. This is sometimes called the singularity, but I don’t like the name too much, since it suggests something special and mysterious is happening. The only thing special going on is that we, humans living on earth in 2009, cannot adequately describe the physics there. Thinking in a slightly less anthropocentric way is, I would think, a good habit when you’re doing physics (but I may be behind the times on this).
Since the collapsed star is extremely dense, the escape velocity is extremely high. The denser it becomes, the more difficult it is too leave. At some stage (but long before we have to plead ignorance and start using fancy sounding words), the escape velocity exceeds the speed of light, so nothing at all can escape. Hence the clever name (black hole, got it?). A classical black hole is distinguished by having an horizon: if you are slightly inside the horizon, you are bound to the collapsing star, sharing the same fate without ever being able to escape.
For an observer staying far from the collapsed star, and in particular one staying outside the horizon at all times, the picture is more elaborate, especially when we take quantum effects into account. I’ll concentrate mainly on observers like those, because we know a lot more about them (or should I say us?). Far away from the black hole gravity is weak, so we have every right to expect that quantum mechanics as we know it describes the experience of those observers faithfully (as usual, by quantum mechanics I really mean quantum field theory, which is our best description of nature as we know it).
On the other hand, in-falling observers will inevitably (sooner or later) experience strong quantum gravity effects, for example time will likely end for them, whatever that may mean. In short, it may be pretty tricky to use our experience, and our best theories, to infer anything about the experience of in-falling observers. Let’s leave that to the very end, as that issue is still not very well-understood (at least not by me).
So, to be conservative, let’s discuss first observers staying at a safe distance from the black hole at all times, and describe what a classical or a quantum black hole looks like for them. One important fact is the following: when observing objects falling towards the horizon, the curved spacetime metric means that the local time is dilated with respect to yours. The time dilation factor becomes infinite as the objects approach the horizon. That is the reason why black holes were referred to, before John Wheeler came up with that clever catch phrase, as “frozen stars”. I like this name a lot, since this is exactly how the situation looks to us, the asymptotic observers, at least classically. As objects approach the horizon, all their internal processes (as we see them) slow down, they “freeze”.
This also means that as objects approach the horizon, we are able to see their short distance structure, the horizon is effectively a microscope. Because of the time dilation factor, we can now see processes that are normally too fast for us to observe. In a relativistic theory this also means short distance physics, in quantum mechanics this also means high energy physics. It is then plausible that for an adequate understanding of the physics of the horizon, we the asymptotic observers will need to use at least some quantum mechanics. This is where the story gets really interesting, but word count tells me it is probably better to postpone all of that till the next post.