Talk:Killing vector field

message: Killing Field??? Maths is awesome!!! 130.195.2.100 03:50, 8 August 2006 (UTC)
replies: text: We kill vectors there. actually, at the Killing horizon. 67.198.37.16 (talk) 05:08, 8 November 2020 (UTC)
thread_title: Awesome!

message: Is there anyway this article could be edited so somebody without a degree in math can know what the flying flip it is talking about. I would really like to know, but the article is filled with so much math specific jargon it is impossible without first reading 90 other articles. 88.154.199.46 08:34, 8 June 2007 (UTC)
replies: text: It would be a pretty difficult to understand what a Killing field is without knowing what a Riemannian metric is at least. Most people who know that would have or be studying for a degree in mathematics or physics.  There is no jargon in the article that I can see but it does rely on specialist terminology. Fortunately this is wikipedia so you can at least click on the links.Billlion 20:17, 10 June 2007 (UTC)
replies: text: Wondering who wrote that and was surprised to find it was me!  Another answer is to understand what an isometry is eg in Euclidean space a cylinder and  a sphere then a Killing vector field is an infinitesimal isometry. That is a way to give some kind lay explanation. Billlion (talk) 14:33, 27 April 2023 (UTC)
thread_title: What?

message: This article does have an interesting name. 88.154.243.24 08:03, 12 July 2007 (UTC)
thread_title: Interesting name

message: The lead makes it sound like the article is going to discuss both Riemannian and semi-Riemannian space, but there are some results in it that I don't think are true for a non-Riemannian signature. "Negative Ricci curvature implies there are no nontrivial (nonzero) Killing fields." I think this is false for semi-Riemannian spaces. E.g., I think general relativity has cosmological solutions with negative Ricci curvature, but these solutions do have Killing vectors such as spatial rotations.--75.83.69.196 (talk) 05:30, 31 January 2011 (UTC)
replies: text: Yeah, some of those claims feel smelly. 67.198.37.16 (talk) 05:00, 8 November 2020 (UTC)
thread_title: results only for Riemannian spaces?

message: Is there any difference between the generalized Killing vector field (see [] and the fundamental vector field?
89.135.20.50 (talk) 09:04, 19 November 2011 (UTC)
replies: text: Yes, theres a difference. They're more or less unrelated. Killing fields are isometries, fundamental fields are just the action of a Lie group mapped out onto a manifold. They are not really related in any kind of naive, direct sense. I guess there is some weird deeper relationships for symmetric spacess but that's getting off the mark. 67.198.37.16 (talk) 05:04, 8 November 2020 (UTC)
thread_title:  Relation to the fundamental vector field 

message: The paragraph about killing vector fields on 2-fields mentions the two "obvious" fields
:U= \partial_\phi
:V=\partial_\theta. 
This is not what I find on this physics forum thread
If someone has the book mentioned in another thread
 (General Relativity Demystified, McMahon) could double check this paragraph for errors in the (incomplete) calculation?  — Preceding unsigned comment added by 88.215.103.183 (talk) 12:55, 22 December 2020 (UTC)
thread_title:  Killing vector fields on the 2-sphere 

message: The "Killing fields on a 2-sphere" subsection in the article sounds informative but this line is difficult for an uninitiated reader (like myself), confusing or perhaps imprecise:
However, moving off of the equator, the two vector fields \partial_\phi and \partial_\theta are no longer orthonormal, and so, in general one has \left[\partial_\phi, \partial_\theta\right] \ne 0 for a point (\theta, \phi) \in S^2 in general position.
I agree the two vector fields are not orthonormal in general position, but that does not imply the Lie bracket gives non-zero values, and I would think it should vanish where the two vector fields in question are defined.  How could it be possible that the Lie bracket of coordinate vectors should be non-vanishing?
240F:7C:CFB3:1:CF39:4DD5:6DD7:4D5C (talk) 03:49, 19 March 2022 (UTC)
replies: text: You're right, the bracket vanishes since the basis \{\partial_\theta, \partial_\phi\} is coordinate induced. The article is incorrect. The incorrect statement is that \partial_\theta is a Killing field. It can be verified that the \phi\phi component of the Killing equation is non-zero. In fact, there's an intuitive view of why this doesn't conserve lengths: if we flow all points in the \theta direction, they move from the north pole to the south pole. This means the points spread out from the north pole, stretching and distorting the metric there.Zephyr the west wind (talk) 21:27, 6 May 2022 (UTC)
thread_title:  Souldn't the Lie bracket of coordinate vectors vanish?