stingc

Black holes have very very high entropy. There are lots of ways to calculate this, and none of them are all that rigorous, but they all give the same answer (so it seems right). This is a very complicated subject, so I'll only be able to scratch the surface.

The usual intuitive argument starts with looking at what the "state variables" are for a black hole. A static classical gas for example is described by pressure, density, and temperature at equilibrium. These are the only things that are measurable classically, so they define the "state" of the system. Now thinking in terms of molecules, there is not just one configuration that corresponds to a measured pressure, density, temp. There are many microscopic configurations corresponding to a single classical state. Counting this degeneracy gives entropy. A large number of microstates for a given classical state means high entropy. This is usually how entropy is defined. It is only occasionally related to "disorder!"

Anyways, there is a remarkable theorem in general relativity stating that a stationary black hole is completely described by three parameters - mass, angular momentum, and electric charge. A black hole must have some quantum mechanical structure, but nobody really knows what this is since there isn't any good theory of quantum gravity (not molecules this time). It doesn't matter for this argument though. There is some unknown fine structure that has to be there. It could be quantized spacetime "chunks," strings or whatever. Its possible to go to string theory for example, and figure out how many string configurations correspond to a given classical mass, ang mom, and charge, just like I talked about above with gases. This is anything but intuitive. You can get an idea of the same thing by figuring out how many (classical) initial states of a system end up in the same final state.

The initial state of a black hole should be a normal star. Say its in equilibrium. How many parameters describe it? You again have total mass, angular momentum, and charge, but these things can be distributed throughout the star in many ways. It also has different types of matter in different places etc. It takes a lot of information to describe a star even classically. Eventually the star blows up and collapses into a black hole if it is large enough. Now how many different stars will collapse to a black hole with a given mass, ang. momentum, and charge? Since a star has so many parameters associated with it, and a black hole so few, you'd expect a huge number of different types of stars to collapse to the same hole. This implies a large entropy.

(I'm ignoring the not insignificant "state" of ejected matter and radiation from a supernova, but I'm trying to brief)