New paper! You can find some additional discussion on
Cosmic Variance.
What is the entropy of the universe?
Paul Frampton, Stephen D.H. Hsu, Thomas W. Kephart, David Reeb
Abstract: Standard calculations suggest that the entropy of the universe is dominated by black holes, although they comprise only a tiny fraction of its total energy. We give a physical interpretation of this result. Statistical entropy is the logarithm of the number of microstates consistent with the observed macroscopic properties of a system, hence a measure of uncertainty about its precise state. The largest uncertainty in the present and future state of the universe is due to the (unknown) internal microstates of its black holes. We also discuss the qualitative gap between the entropies of black holes and ordinary matter.
Why is the coefficient from the metric (1-2M/r)^-.5 not included in integral of M=M(r) in contrary to integral of entropy. Is this special feature of amd mass?
ReplyDeleteRami Niemi
Univ. Helsinki
Hi Niemi,
ReplyDeleteYes, in the ADM mass formula the factor of $(1-2M/r)^-.5$ is absent. This reflects the negative binding energy of gravity. The fact that the "volume measures" in the integrals for the ADM mass and total entropy S are different is what allows the existence of monsters.
More physically, it has been known for a long time that the negative binding energy of a system can almost cancel the positive rest masses of the constituents. Positivity theorems require that the ADM mass is positive, but it can approach zero. Obviously, if there are many constituent states the entropy can be large, yet the mass of a black hole formed by the system will be small. See gr-qc/9801106 for more discussion and references.
There are also some useful slides in these talks:
http://duende.uoregon.edu/~hsu/talks/monster_caltech.pdf
http://duende.uoregon.edu/~hsu/talks/miami_2007_monsters.pdf
Thank you for the reply and tips Steve and thank you for excellent blog(specially financial topics(hoping that fed rate cut will hold the street til' the evening) evolution and statistics are great).
ReplyDeleteI'm preparing my masters thesis vaguely in field of holography. And monsters are probably part of my work.
Rami Niemi
if.iknisleh@imein.imar
Rami,
ReplyDeleteThanks for your comments and best of luck with your thesis. Feel free to email me if you have questions about monsters.