Talk:Kruskal–Szekeres coordinates

Expert needed?

I see a note that this page needs the attention of an expert. I suppose that it lacks the format commonly found in Wikipedia pages which begins with a high level introduction, followed by substantive content.

I am not an expert, but a borderline specialist. I find the page useful and I am trying to verify some of the technical detail.

It is a bit confusing that there are two variables 'r'—one from classic Schwarzschild metric, and one implicitly defined for the Kruskal-Szekeres line element. Perhaps they are the same.

--NormHardy 20:12, 13 August 2006 (UTC)[reply]

The two r are the same (unless I'm misunderstanding your question) — the Schwarzschild coordinate. JanBielawski 21:39, 28 September 2006 (UTC)[reply]

Question, maybe a suggestion

How can it be seen that the Kruskal-Szekeres metric has an horizon? It could be useful to indicate that. Similarly, in the article on Schwarzschild metric, the horizon seems obvious because of the apparent singularity. But what is the real way to look for an horizon in a metric?

(Partial) answer. It depends what kind of horizon you are looking for. Event horizons are often tricky to find generally. In stationary spacetimes they coincide with Killing horizons, which are easy to find if you know what the Killing vectors are since the norm of a vector is an invariant. In general spacetimes, one (slow) way to find the event horizon numerically is just to propagate lots of null shells through the metric and see where they end up. Apparent horizons are also reasonably easy to locate. Pick a spacelike hypersurface, choose a compact two-surface within the hypersurface and see if the null normals have zero expansion. In Schwarzschild (in any coordinates) the event horizon can be found by looking at where the expansion of radially outgoing null geodesics is zero.

Too much math talk ?

Topics like these make me wonder, to some the math may be clear, but why not a description of what the scientist had in mind perhaps some images??? Words are a language to me, math is only rules but in itself it doesnt form a story to me, while wiki is suposed to explain. —The preceding unsigned comment was added by 82.217.143.153 (talk) 01:46, 14 January 2007 (UTC).[reply]

Dimensionality of the singularity

On 6 May 2008, TimothyRias (talk · contribs) removed the sentence "Note that in these coordinates the curvature singularity is in fact represented by a curved line, that is, it is one dimensional.". He justified this by saying that "dimensionality of the singularity is pretty much undefined. If anything it is either 0 or 3 dimensional". The curvature is finite except at the singularity which occurs at r=0. As one approaches r=0, the contributions of variations in the co-latitude and longitude to the line element become zero because of the factor of r² in $r^{2}d\Omega ^{2}$ . As the article correctly says the "curvature singularity is given by the equation UV = 1". Thus one of U or V may be varied freely (with the other determined thereby) while remaining at the singularity. Thus three dimensions have either been constrained or rendered null while one dimension remains. In other words, the singularity is one dimensional. JRSpriggs (talk) 17:21, 7 May 2008 (UTC)[reply]

Noteworthy

"The Kruskal-Szekeres coordinates do not describe a coordinate patch that covers a part of the gravitational manifold that is not otherwise covered - they describe a completely different pseudo-Riemannian manifold that has nothing to do with Einstein’s gravitational field (Abrams 1980; Loinger 2002; Crothers 2006). The manifold of Kruskal-Szekeres is not contained in the fundamental one-to-one correspondence between the E^3 of Minkowski space and the M^3 of Einstein’s gravitational field, and is therefore a spurious augmentation." Spherically Symmetric Metric Manifolds, Stephen J. Crothers, Page 17, http://www.aias.us/documents/otherPapers/BlackHoleCatastrophePRS.pdf —Preceding unsigned comment added by 91.35.102.189 (talk) 05:56, 18 September 2008 (UTC)[reply]

All of Crothers' papers seem to have been published in Progress in Physics, a fringe journal on which Crothers himself serves as an editor. I don't think this is any better than not being published at all. And the content is wrong; he doesn't seem to understand that r is just a variable that can be defined however one wants, and happens, in the case of Schwarzschild coordinates, to be defined as the reduced circumference. -- BenRG (talk) 12:53, 18 September 2008 (UTC)[reply]

Mislabeled axes?

In the Kruskal-Diagram, the axes are labelled as if it were a plot of V versus U. But if I'm not mistaken, it is actually of T vs R. Hurkyl (talk) 19:43, 1 January 2009 (UTC)[reply]

I rather think that the article is mislabeled. Usually, its called u and v instead of T and R (see Misner, Thorne and Wheeler - Gravitation p. 827, or Hartle - Gravity p. 270). --Allen McC. (talk) 07:28, 3 January 2009 (UTC)[reply]

I changed the notation in the article to match the first two diagrams, and to match the convention in Gravitation (except I used uppercase U and V as in those diagrams, whereas Gravitation uses lowercase) Hypnosifl (talk) 18:06, 23 April 2010 (UTC)[reply]

Proposed notation change

I note from the above that the notation was changed two years ago, mainly, it seems, to match a diagram that no longer is in this article. I would like to propose a change back from (U,V) to (T,R) for several reasons:

If a coordinate is timelike everywhere it seems to me to make sense to use a letter such as T to represent time. Similarly R seems appropriate for an everywhere-spacelike coordinate.
Usage in the literature seems mixed. While some use (u,v) others do use (T,R) (t,r) or similar. For example Rindler's Relativity: Special, General and Cosmological uses (t,x).
This usage would be similar to the use of (T,X) for Minkowski coordinates in the Rindler coordinates article. The relationship between Minkowski coordinates and Rindler coordinates bears many similarities to the relationship between Kruskal–Szekeres coordinates and Schwarzschild coordinates, and it would be easier to make this connection if the two articles used similar notation.
I am in the process of creating a new diagram to replace the yellow one at the beginning of this article (and a matching one for the Rindler coordinates article), and I can label the diagram with whatever letters are agreed, so compatibility with diagrams need not be an issue.

Anyone object to my proposal? -- Dr Greg talk 19:16, 10 November 2012 (UTC)[reply]

I would suggest (T,X), and using (U,V) for the lightcone variant. The coordinate r is still going to be appearing all over the place, so I think it is a bit clearer to prefer against using R. At least (T,X) is harder to conflate with (t,r) than (T,R) is. (It also avoids some interpretational baggage: a radial coordinate normally doesn't continue through zero meaningfully.) Cesiumfrog (talk) 23:33, 10 November 2012 (UTC)[reply]