- #1

marcus

Science Advisor

Gold Member

Dearly Missed

- 24,770

- 791

there is a curious 1996 paper by Rovelli that gets the

black hole entropy/area formula by a simple counting method.

I say simple advisedly---a lot of combinatorics and counting is

not really simple at all but IMHO difficult---but in this amazing little

5 page paper the counting of partitions of a number, which is all it really is, really is simple

and like so much other combinatorics and elementary arithmetical jazz the golden mean shows up, so he is finding the BH entropy using the logarithm of the golden mean---got a chuckle out of that for some reason

well, here's the link if you want a look

http://arxiv.org/gr-qc/9603063 [Broken]

notice that he was just looking at a Schwarzschild hole, looking at the simplest thing he could, and oversimplifying indeed IMO not even paying attention like riding a bicycle with your eyes shut and the amazing thing is that his was one of the very first papers (either in string or loop) and he came within a factor the size of the, say, immirzi parameter (which he was ignoring). such things are governed by a kind of graceful luck I believe.

For comparison here is a 1996 string paper which is the first

instance of a string explanation.

http://arxiv.org/hep-th/9601029 [Broken]

It is by Strominger and Vafa and applies to 5-dimensional "extremal" holes by counting the degeneracy of "BPS soliton"

bound states.

Marcus

_______________

A foxhunt by British gentry has been described as "the unspeakable in pursuit of the inedible"

black hole entropy/area formula by a simple counting method.

I say simple advisedly---a lot of combinatorics and counting is

not really simple at all but IMHO difficult---but in this amazing little

5 page paper the counting of partitions of a number, which is all it really is, really is simple

and like so much other combinatorics and elementary arithmetical jazz the golden mean shows up, so he is finding the BH entropy using the logarithm of the golden mean---got a chuckle out of that for some reason

well, here's the link if you want a look

http://arxiv.org/gr-qc/9603063 [Broken]

notice that he was just looking at a Schwarzschild hole, looking at the simplest thing he could, and oversimplifying indeed IMO not even paying attention like riding a bicycle with your eyes shut and the amazing thing is that his was one of the very first papers (either in string or loop) and he came within a factor the size of the, say, immirzi parameter (which he was ignoring). such things are governed by a kind of graceful luck I believe.

For comparison here is a 1996 string paper which is the first

instance of a string explanation.

http://arxiv.org/hep-th/9601029 [Broken]

It is by Strominger and Vafa and applies to 5-dimensional "extremal" holes by counting the degeneracy of "BPS soliton"

bound states.

Marcus

_______________

A foxhunt by British gentry has been described as "the unspeakable in pursuit of the inedible"

Last edited by a moderator: