A must read post on black hole entropy by physicist (Perimeter Institute) and blogger Sabine Hossenfelder! ;-)
Now that she mentions it, "Entropy" is a cool name for a kid (superhero?), maybe even cooler than "Max Talmud" :-)
These days, everybody is talking about entropy. In fact, there is so much talk about entropy I am waiting for a Hollywood starlet to name her daughter after it. To help that case, today a contribution about the entropy of black holes.
To begin with let us recall what entropy is. It's a measure for the number of micro-states compatible with a given macro-state. The macro-state could for example be given by one billion particles with a total energy E in a bag of size V. You then have plenty of possibilities to place the particles in the bag and to assign a velocity to them. Each of these possibilities is a micro-state. The entropy then is the logarithm of that number. Don't worry if you don't know what a logarithm is, it's not so relevant for the following. The one thing you should know about the total entropy of a system is that it can't decrease in time. That's the second law of thermodynamics.
It is generally believed that black holes carry entropy. The need for that isn't hard to understand: if you throw something into a black hole, its entropy shouldn't just vanish since this would violate the second law. So an entropy must be assigned to the black hole. More precisely, the entropy is proportional to the surface area of the black holes, since this can be shown to be a quantity which only increases if black holes join, and this is also in agreement with the entropy one derives for a black hole from Hawking radiation. So, black holes have an entropy. But what does that mean? What are the microstates of the black hole? Or where are they? And why doesn't the entropy depend on what was thrown into the black hole?
While virtually nobody in his right mind doubts black hole have an entropy, the interpretation of that entropy is less clear. There are two camps: On the one side those who believe the black hole entropy counts indeed the number of micro-states inside the black hole. I guess you will find most string theorists on this side, since this point of view is supported by their approach. On the other side are those who believe the black hole entropy counts the number of states that can interact with the surrounding. And since the defining feature of black holes is that the interior is causally disconnected from the exterior, these are thus the states that are assigned to the horizon itself. These both interpretations of the black hole entropy are known as the volume- and surface-interpretations respectively. You find a discussion of these both points of view in Ted Jacobson's paper "On the nature of black hole entropy" [gr-qc/9908031] and in the trialogue "Black hole entropy: inside or out?" [hep-th/0501103].
A recent contribution to this issue comes from Steve Hsu and David Reeb in their paper
Black hole entropy, curved space and monsters
Phys. Lett. B 658:244-248 (2008)
...read the rest...
See related post here, with nice pictures.