Talk:Linearized gravity

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I propose that weak-field approximation be merged into linearized gravity, as the former is too technical to stand as an article in it's own right and would fit in nicely with the latter, which I can see as developing into a fairly comprehensive article. ---Mpatel (talk) 10:06, 15 October 2005 (UTC)Reply

I agree that the material so far could be merged, but there is a lot of ground to cover. I just added a preliminary todo list with some suggestions. ---CH 00:33, 6 February 2006 (UTC)Reply

One other point: possibly linearized gravity should be a redirect to linearized general relativity since other theories also have their linearized approximations? Actually, weak-field theory (general relativity) might be a more standard name. ---CH 00:49, 6 February 2006 (UTC)Reply

On the talk: Linearised Einstein field equations discussion, I just added a note I'm not sure why we have separate articles on Linearized Gravity and Linearised Einstein field equations; any reason not to merge them? Geoffrey.landis (talk) 16:07, 14 August 2008 (UTC) See note below. Geoffrey.landis (talk) 14:22, 23 August 2008 (UTC)Reply

As a courtesy, I have removed the "expert" items from todo list. I am leaving WP and doubt anyone else will know how to implement the suggested improvements since this was mostly a note to myself.

Sadly, I am now abandoning this article to its fate. See User:Hillman/Archive for the last version I edited. I emphatically do not vouch for anything you might see in more recent versions.

Unfortunately, I have reason to believe that at least some future versions of this article are likely to contain slanted information, misinformation, or disinformation, particularly regarding

1. pseudoscience topics such as
   • anti-gravity
   • electrogravity
   • Podkletnov "effect" (sic)
2. fringe physics topics such as
   • plasma cosmology
   • Felber "effect" (sic; actually a coordinate effect, not a physical effect)

Be careful in following external links to outside websites, which may be cranky and which may do likewise.

Good luck to all students in your search for information, regardless!---CH 01:46, 1 July 2006 (UTC)Reply

I merged the entire content of the (former) Linearised Einstein field equations article here. I didn't see any reason for two separate articles on Linearized Gravity, since they cover similar or identical ground, and nobody seemed to object when I proposed it on the talk page of both articles, so it's now done. (I inserted the text whole, making no changes; so there may be some rewriting needed to smooth it out). Geoffrey.landis (talk) 14:26, 23 August 2008 (UTC)Reply

It would be very helpful to explain the effect on square root of the determinant when perturbing the metric.TonyMath (talk) 04:16, 30 May 2015 (UTC)Reply

See Post-Newtonian expansion#Expansion in h. To the first order,

${\displaystyle {\sqrt {-g}}\approx 1+{\tfrac {1}{2}}h_{\alpha \beta }\eta ^{\beta \alpha }\,.}$

OK? JRSpriggs (talk) 07:31, 30 May 2015 (UTC)Reply

Nice but I am aware of a more general result: for ${\displaystyle g_{\mu \nu }=b_{\mu \nu }+h_{\mu \nu }}$ then ${\displaystyle {\sqrt {-g}}={\sqrt {-b}}~(1+{\tfrac {1}{2}}h_{\mu }^{\mu }+{\tfrac {1}{8}}h_{\nu }^{\nu }h_{\mu }^{\mu }-{\tfrac {1}{4}}h_{\nu }^{\mu }h_{\mu }^{\nu }\ldots )}$. This is valid for any background metric ${\displaystyle b_{\mu \nu }}$ not just flat-space. It was derived with Mathematica on this website forum but I'd love a reference.TonyMath (talk) 04:54, 4 June 2015 (UTC)Reply

I am glad that someone else has confirmed the formula I got. I cannot help you find a reference since I am no longer plugged into academia. JRSpriggs (talk) 04:16, 5 June 2015 (UTC)Reply

I have come across papers referring to the graviton as the transverse-traceless part of the metric ${\displaystyle g_{\mu \nu }}$. Nowhere do I find mention of this, whether in the section on the graviton nor on gravitational radiation. Since this site mentions the metric per se, it might make sense to put some discussion here? In particular, I would like to know if this is the only manifestation of the graviton. TonyMath (talk) 15:21, 4 June 2015 (UTC)Reply

I do not think that it is possible in general to separate the metric into a static background and a perturbation in the form of radiation. However, if such a separation can be made, then I believe that it is true that the perturbation will be transverse (perpendicular to the direction of motion) and traceless relative to the background. JRSpriggs (talk) 04:23, 5 June 2015 (UTC)Reply

Thank you but I would like some clarification. There is a body of work out there which makes this type of separation, e.g. the Lecture Notes of GRT by S. Carroll in the weak field approximation - though I would like a book reference (anyone?). My dumb question: in such a case why Transverse- Traceless (TT)? Is it because only the TT property allows such the graviton to be treated as perturbation? or are you perhaps making an analogy with Electromagnetic radiation? At any rate, should a few additional text sentences be warranted on this subject? TonyMath (talk) 07:37, 5 June 2015 (UTC)Reply

Hey all who are interested. I was unsatisfied with the page given it's rather overbearing equations with little to no detail or explanations, so I decided to provide more cleaner discussion on the topic using Carroll for reference. I also simplified the language and notation used to describe gauge symmetry in the linearized field equations since the section that existed used very obtuse notation and did little to connect to the underlying physics. Cjayross (talk) 05:17, 24 June 2019 (UTC)Reply

What sign convention is assumed? The sign in the equation of motion for the metric perturbation depends on this. — Preceding unsigned comment added by Jcline1 (talk • contribs) 10:16, 2 December 2024 (UTC)Reply