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- Just for the record – if Sir Nicholas de Mimsy-Porpington wasn't listed as the original creator of JRSpriggs' userpage (by making this edit back in 2007), then JRSpriggs would receive an automatic notification, by Twinkle, about the ongoing MfD nomination. As can be seen, the notification ended up here. — Sundostund mppria (talk / contribs) 15:40, 9 November 2022 (UTC)
Schwarzschild metric
Hi JRSpriggs!
I recently edited the Schwarzschild metric page. The main change was to make the domain of definition of the metric more precise. I thought this would be nice as the domain of definition is known exactly, while on the page it is only described as a subset of a certain space, and a reader might reasonably ask which subset. However, my changes ended up affecting other parts of the article, which may not have been helpful.
Do you think there is a good way to make the domain of definition precise, while keeping in all the other details?
Zephyr Zephyr the west wind (talk) 10:53, 24 November 2022 (UTC)
- This article deals with two things: the Schwarzschild metric and the coordinate system. The metric is the main topic and other coordinate systems are mentioned. So the metric is not being defined relative to R4. The metric exists at the horizon as well as the exterior, when the physical conditions are appropriate i.e. vacuum and spherical symmetry.
- I see no justification for your claim that the signature is (+ - - -) rather than (- + + +). JRSpriggs (talk) 20:11, 24 November 2022 (UTC)
- Thanks for the response. Regarding the signature, writing mostly minus when it should have been mostly plus was certainly a slip on my part. Clearly I've been doing too much particle physics recently.
- I didn't mean to suggest that the metric is defined relative to , but rather that the Scharzschild metric in Schwarzschild coordinates is well defined on two patches of an underlying Schwarzschild manifold, which in local coordinates are given by open subsets of . But using the spherical symmetry the open subsets can be replaced with an open subset of times the sphere.
- I see what you mean by dealing with the metric first, then the coordinate system. The space described, is the underlying manifold. But then the metric is well defined as a tensor field on this whole space (e.g. using incoming Eddington–Finkelstein coordinates), so the '(on a subset of)' remark is misleading in this context. It's really just the '(on a subset of)' which I take issue with, and wish to make more precise. Zephyr the west wind (talk) 10:35, 25 November 2022 (UTC)
- The meaning of "subset" is clarified a couple sentences later by "The Schwarzschild metric is a solution of Einstein's field equations in empty space, meaning that it is valid only outside the gravitating body.". JRSpriggs (talk) 04:59, 26 November 2022 (UTC)
- Then why not say for earlier? Besides, it is also legitimate to study the Schwarzschild black hole, which has no outside, and for which the domain of definition of the metric extends to the interior. Sure, this is mentioned in the coordinate system part, but the initial discussion seems to suggest that it is necessary to patch the Schwarzschild solution with an interior solution. Zephyr the west wind (talk) 11:06, 26 November 2022 (UTC)
- The meaning of "subset" is clarified a couple sentences later by "The Schwarzschild metric is a solution of Einstein's field equations in empty space, meaning that it is valid only outside the gravitating body.". JRSpriggs (talk) 04:59, 26 November 2022 (UTC)
- If you want to make a change, then do it rather than trying to talk me into doing it. Of course, any change you make may be reverted or further changed by me or someone else. That is the way Wikipedia works.
- I would prefer that you make small localized changes, then wait a day or two for other people to respond or not, before making another small change.
- There is not just one interior solution. There is the solution where the future is in the +r direction, a "white" hole. And there is a solution where the future is in the -r direction, a black hole. They are not directly connected to each other, but they both could join to the same exterior solution. However, such a white hole converting to a black hole seems highly unphysical to me. JRSpriggs (talk) 02:17, 27 November 2022 (UTC)
- Sorry, thanks for the advice. Happy editing! Zephyr the west wind (talk) 10:15, 28 November 2022 (UTC)
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