Talk:Schwarzschild metric

From Wikipedia, the free encyclopedia

	This article is within the scope of WikiProject Physics, which collaborates on articles related to physics.	Physics Portal
???	This article has not yet received a rating on the assessment scale. [FAQ]
???	This article has not yet received an importance rating within physics.
Help with this template Please rate this article, and then leave comments here to explain the ratings and/or to identify the strengths and weaknesses of the article.

Contents 1 Content split 2 Units? 3 Merge from Schwarzschild black hole 4 Isotropic coords? 5 Controversy 6 Proposed merge from Deriving the Schwarzschild solution

[edit] Content split

I've taken out a chunk of this article and extended it to give a more detailed derivation of the Schwarzschild metric in deriving the Schwarzschild solution (for those interested in such things). —The preceding unsigned comment was added by 139.133.7.37 (talk • contribs) on 16:32, 29 March 2005.

[edit] Units?

Not setting c = 1 in articles on general relativity seems completely ridiculus, for any number of reasons. I can see how, pedagogically, one might wish to do that in articles on special relativity (although I personally object). By the time someone is comfortable with reading articles on general relativity, however, they should be comfortable with the idea of natural units. In the interior of a Schwarzschild black hole the t and r coordinates become spacelike and timelike respectively. Are we now measuring time in meters and space in seconds, or do we suddenly switch the units of t at the event horizon??? -- Fropuff 1 July 2005 15:38 (UTC)

Whether you think it's "completely ridiculous" is not really the point. True, when someone is comfortable with reading GR articles, putting c=1 simplifies the equations etc. Putting c=1 or not has nothing to do with the nature of the coordinates; only the metric signature determines that. Let's agree that if a mathematical quantity is spacelike, this means that its inner product with itself is +ve; this does not necessarily mean that the quantity is measured in units of metres !!! For example, in GR, consider the four-velocity of a material particle: it's inner product with itself is always negative, but four-velocity is not measured in metres or seconds !!! Anyway, for someone who first comes across this article (and who isn't a specialist, but may have heard of black holes etc.), they're probably wondering why the units are messed up in the metric. In other articles where this metric is mentioned, I agree that putting c=1 is ok, as long as this is stated (like in some of the GR articles). Specialists have this tendency to be as elegant as possible, but they sometimes overlook the fact that not all articles are intended for them. We should remember this. --Mpatel 11:32, 17 July 2005 (UTC).

I actually came over into the Talk section here because I was rather surprised to see that the article was not using natural units. I think it's reasonable to use natural units in the article as long as we mention that is what we're doing. An explanation as to why this makes sense even beyond just simplifying the equations (i.e. treating space and time as equivalent geometric quantities, etc.) would also be appropriate. This will serve to keep the article in sync with current practice in the field while still educating and providing an introductary path for newcomers. 72.130.178.52 04:33, 5 December 2006 (UTC)

It is mentioned elsewhere (on Kerr metric page, for example) that time and space inside horizon swap. It would be nice if this will be explained a bit.

—The preceding unsigned comment was added by 195.66.192.167 (talk • contribs) on 11:04, 17 July 2005.

In 1-dimensional spacetime (one spatial coordinate) Schwarzschild metric is (in natural units, c=1)

ds^2 = -(1-rs/r)*dt^2 + dr^2/(1-rs/r)

where rs - Schwarzschild radius.

Let's use a = (1-rs/r). r belong to [0,+inf) -> a belong to (-inf,1).

ds^2 = -a*dt^2 + dr^2/a

Null geodetics (ds^2=0):

dr^2 = a^2*dt^2 (again, remember that -inf<a<1)

I've made a picture with light cones and wordlines of photons, see http://195.66.192.167/linux/blackhole_1d.gif (feel free to add it to wiwkipedia, I am new and do not ko=now how to upload it). '+' signs show 'future': regions where ds^2 > 0 (and how mathematically future is different from past? both have ds^2 > 0...).

It visualizes the following:

1) photon will never reach horizon in 'our' (distant observer's) frame of reference.

2) inside horizon directions where ds^2 > 0 are spacelike. (time and space are swapped).

Open questions:

1) I placed '+' inside horizon so that light is falling into singularity and not away from it to horizon, but this is a bit arbitrary. Is there solid reason why it is so?

2) Will photon which is somehow got inside horizon ever reach singularity in our frame of reference? I think it wouldn't, exactly like 'external' photons could not reach horizon due to time dilation. I infer time dilation from ever shrinking angle of light cone when light approaches horizon from outside or when it approaches singularity.

—The preceding unsigned comment was added by 195.66.192.167 (talk • contribs) on 11:58, 17 July 2005.

cool you just answered my question on the solution inside the black hole. but then we'd have 3 dimensons of time and 1 space!? wat does that mean? anyway i dont think its legitmate to solve it inside the horizon. quantum effects are likely to dominate (dunno about just below the horizon) —The preceding unsigned comment was added by Protecter (talk • contribs) on 11:14, 25 October 2005.

[edit] Merge from Schwarzschild black hole

Merger sounds good. ---Mpatel (talk) 18:21, August 30, 2005 (UTC)

I agree. I'll go ahead and do it.--Bcrowell 03:15, 3 September 2005 (UTC)

[edit] Isotropic coords?

Can someone add pretty language about isotropic coordinates? That is,

so that

or should I just uncermoniously copy this into the article at some point? I don't think I can say anything intelligent about these coords. linas 20:19, 29 October 2005 (UTC)

Hmm, there's an article isotropic coordinates which doesn't mention this form, and this article doesn't link.linas 20:49, 29 October 2005 (UTC)

Hmm, can the above be called the "standard isotropic Schwarzschild coords" or something like that? Then the above formulas can be added to the article on isotropic coords, and this article can then be made to link to that. ?linas 21:09, 29 October 2005 (UTC)

[edit] Controversy

There is a controversy between the Schwarzschild Model for the Black Hole and the E=mc2 equation. I will be starting an article on this soon. Even better, someone help me start it. I really don't have that much time. Freddie 02:23, 20 February 2006 (UTC)

If this article contains your own thoughts on the matter, be advised that it is "original research", and will likely be deleted very quickly as a result (Wikipedia is only supposed to summarize information found elsewhere, not be a place to post new information). If you have questions about how the Schwarzschild metric and aspects of general relativity (like the mass/energy equivalence) relate to each other, a suitable place to discuss this is either on this talk page, or at Talk:General relativity). --Christopher Thomas 04:26, 20 February 2006 (UTC)

[edit] Proposed merge from Deriving the Schwarzschild solution

This merge was proposed on 3 March 2006 by User:Hillman. I've created this heading so that we can figure out if people want the merge to occur. --Christopher Thomas 20:40, 27 August 2006 (UTC)

• Oppose. I think the derivation is long enough that it's reasonable to put it in its own article to avoid clutter in this one. --Christopher Thomas 20:40, 27 August 2006 (UTC)
• Oppose. The derivation is indeed a lengthy one, which deserves its own article. Since the main article is (for the most part) qualitative, adding the derivation will not add significantly to the content of the article. --Masud 17:59, 25 September 2006 (UTC)