What are Kruskal-Szekeres Coordinates in Relation to a Static Black Hole?

[stevebd1]

I'm currently looking at Kruskal-Szekeres coordinates in relation to a static black hole.

For the exterior region, the coordinates are-

$$R=\left(\frac{r}{2GM}-1\right)^{1/2}e^{r/4GM}cosh\left(\frac{t}{4GM}\right)$$

For the interior-

$$R=\left(1-\frac{r}{2GM}\right)^{1/2}e^{r/4GM}sinh\left(\frac{t}{4GM}\right)$$

where c = 1 and G, the gravitational constant, is kept explicit.

I've looked extensively on the web but can find very little as to explaining the equations in a bit more depth. I'd appreciate it if someone could shed some light on what e represents and while I'm certain that c^2 appears adjacent to r in the first set of brackets, does it appear anywhere else in the equations? Also, would it be correct to assume that t represents time?

 

[Wallace]

Check out http://casa.colorado.edu/~ajsh/schwp.html" site. It goes through the various co-ordinate representations of black holes and has some nice animations as well. I think it should answer your question.

 

[stevebd1]

Thanks for the link Wallace. I also found a paper that covered the subject 'Kruskal Coordinates and Mass of Schwarzschild Black Holes by' Abhas Mitra-

http://arxiv.org/abs/astro-ph/9904162

Unfortunately, neither actually state what the quantities e and t are, I can only assume that e is energy and t is time but don't see how they would be incorporated into the equations. It appears to be taken for granted that e and t are understood but would appreciate confirmation as to what they are.

 

[Wallace]

t is time, though of course it is a different time co-ordinate to that appearing in the Schwarzschild metric. I'm pretty sure that the e is just http://en.wikipedia.org/wiki/E_%28mathematical_constant%29" (i.e. the same e as in Log_e = Ln).

 

[George Jones]

Thanks for the link Wallace. I also found a paper that covered the subject 'Kruskal Coordinates and Mass of Schwarzschild Black Holes by' Abhas Mitra-

http://arxiv.org/abs/astro-ph/9904162

Careful; the main results of this infamous and unpublished paper are quite wrong.

 

[stevebd1]

Thanks for the heads up George, I was under the impression that if a paper was on the arxiv website then it had passed some seal of approval, that doesn't appear to be the case; I'm assuming that Kruskal-Szekeres coordinates are still legite though. Regarding e being a constant and probably the log of something, what exactly would it be the log of?

 

[stevebd1]

I twigged within a couple of minutes of my reply that e is a constant as stipulated in the wikipedia link; Physics Forums appears to undergo some kind of maintanence around 7.45 and 8.15 am GMT (which would be around midnight PDT) so I couldn't edit my post. Does anyone have an idea of how time would be incorporated as t?

 

[saturn]

Careful; the main results of this infamous and unpublished paper are quite wrong.

hello, i would like to know what result in the paper is wrong? it is the transformation itself?

 

[Wallace]

I haven't read that paper in detail, but from the abstract it is drawing physical significance from the properties of a particular co-ordinate system. This is a big no no! Anything with physical meaning will be invariant (not co-ordinate dependant). So for instance, you should be able to demonstrate what that paper claims to show in the Schwarzschild co-ordinate system, or any other of the many BH co-ordinate charts.

 

[Wallace]

I was under the impression that if a paper was on the arxiv website then it had passed some seal of approval, that doesn't appear to be the case.

I realize this is an old post, but since the thread has been bumped anyway...

The fact that a paper appears on arxiv really doesn't signify very much. It doesn't mean that it has been peer-reviewed. There is a level of moderation of arxiv postings, but it is not very strict. (That is in no way a criticism of arxiv, I'm just saying how it is).

More generally, even if something is peer-reviewed, that still doesn't mean that the contents of the paper are now considered to be the new standard. This is a very common misconception about peer review. The real peer review comes after a paper has been published and the whole community can read, respond, cite or ignore the paper depending upon the arguments it presents. The formal review process prior to a paper's publication simply ensures that the arguments are clear and free of obvious mistakes, any data are presented with sufficient detail to understand possible sources of error and that relevant prior work has been considered and responded to if necessary. A referee doesn't even have to agree with a paper's conclusions in order to pass it for publication.