Hi, I have a question about Black Holes. I read that they are objects of maximum entropy for that particular region of space. So, does this apply to a singularity such as in the beginning of the Big Bang theory? If the singularity at the beginning of the Big Bang had maximum entropy, how does the universe exist as it does today?
Penrose has argued along these lines to point out that by virtue of the Second Law our understanding of the bigbang must be flawed. I heard him give a talk which was largely about this, and he could not resolve the difficulty to his satisfaction. However it is not true that a black hole singularity looks like the big bang singularity. they are very different. a singularity is just a region where the theory breaks down, generates infinities, goes kaput. a singularity can be pointlike (extending only in time) or it can be an unbounded 3D region extending to infinity spatially but with no duration in time. I am not sure that one can make a good analogy between black hole singularity and big bang. MAYBE one can. But for me it is not clear enough so I cannot see how to apply the Second Law. I hope you get some answers to your question because it is an interesting one. Good luck
IIRC, hawking compared the two in his PhD thesis.. But I don't remember what results he came up with. :uhh:
It's not clear to me what the Schwartzschild radius of a supposed black-hole-like big bang singularity would be.
This comes up often enough to be a FAQ http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html The quick summary of the FAQ is that the universe is not a black hole, because the singularity is at the beginning of time. Not only is the universe not a black hole, there's no reasonable way to make it a black hole, because the singularity is at the wrong time. The standard cosmologies don't have the universe as a white hole (time reversed black hole) either, but it turns out to be possible to construct such a cosmology. It turns out that a white hole under certain conditions can be indistinguiishable from the standard FRW cosmologies for a long time (though not forever).
The answer to your question may be as follows : The entropy at the end of the period of inflation was maximal for a universe in which gravity is not the dominant force (inflation was the dominant force up to then) - ie a homogeneous universe of mass-energy. But as inflation ended, gravity became dominant and a homogeneous universe of mass-energy is no longer the maximal entropy state in a gravity-dominated universe. See also the thread on Weyl Curvature Hypothesis & Entropy : https://www.physicsforums.com/showthread.php?t=48076&page=2&pp=15