# Talk:Maxwell's equations in curved spacetime

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## spacetime is dynamic

It's true that general relativity dictates that spacetime be dynamic. But nowhere in this article is any use made of that assumption. It seems pretty irrelevant, so I'm removing it. And adding something to the intro to suggest that we actually still have the same equations. -lethe talk + 22:15, 5 April 2006 (UTC)

OK, I understand now why the intro wants to mention that spacetime is dynamic, and why it is relevant. The fact that spacetime must get a curvature from the electromagnetic field means that there is no such thing as Maxwell's equations in flat spacetime. I don't think the intro made that clear before (I didn't realize that's what it was saying, for example), and I've tried to improve that.
The intro still had problems though: the equations presented in this article are not really a generalization of Maxwell's equations, unless you restrict the meaning of the phrase "Maxwell's equations" to mean only that form of the equations you learned as an undergraduate. Introducing an explicit metric dependence is useful even when you want to do Maxwell's equations in spherical coordinates on flat spacetime. It is the first step towards a coordinate independent formulation. Once you do have your coordinate independent formulation, you see that actually, Maxwell's equations are exactly the same in curved spacetime. I've rewritten the intro to try to reflect this view. -lethe talk + 16:37, 6 April 2006 (UTC)
I knew there were some iffy issues regarding generalisation, approximations etc. of Max. Eq.'s. I didn't want to mention them right at the start of the article, as that's not where these technical issues belong. But your rewriting of the intro. is good - you've worked well around these issues whilst keeping the important points where they should be. MP (talk) 09:52, 7 April 2006 (UTC)

## formatting

I didn't like some of your formatting changed, Mpatel. For starters, the Manual of style suggests (and I agree) that we shouldn't start a sentence with a math symbol (you start one clause with a *). Also, I really don't like inline tex, so I'm changing that back. Finally, you changed the equation from *d*F = j to d*F = *j. As far as I can tell, one of these equations must be wrong by a minus sign, since *2=–1 on two forms in any spacetime with signature 1. I thought that the first equation was the proper one, but I'm not positive. I guess I'd like to get straight on that. -lethe talk + 17:35, 8 April 2006 (UTC)

## Black hole lensing gif

It should be common sense that a 10 mb picture shouldn't be on the front page. I don't really care to start an edit war over it.

## Index naming

Latin indexes are, by convention, only used spatial dimensions (x,y,z). Greek indexes conventionally run over all spacetime dimensions (t,x,y,z). So, I'm going to change latin indexes to greek where applicable (which is pretty much everywhere). Well.caffeinated 21:59, 22 August 2007 (UTC)

Mpatel, why did you reverse my changes? Was anything wrong? I actually see something wrong with the current version. In the section Relationship between Christoffel symbols and the metric tensor, the last equation is wrong. It should have a negative or the indeces should be switched on the electromagnetic tensor. My changes corrected this.

In my changes I also added how maxwell's equations can be derived from an action to give the equation: ${\displaystyle J^{\mu }={1 \over {\sqrt {-g}}}\partial _{\nu }\left({\sqrt {-g}}F^{\mu \nu }\right)=D_{\nu }F^{\mu \nu }\!}$. I also intended to show how the christoffel symbols relate to this form of the equation.

So what do you disagree with?

Well.caffeinated 22:36, 22 August 2007 (UTC)

## Missing something??

the first two things that that i looked for when first encountered this article was: 1) derivation of the curved maxwell equations from the vacuum maxwell equations...via covariant derivatives; and 2) a comparison of the curved maxwell equations to the einstein field equations. i don't understand why all the other stuff in the article is more relevant, am i missing the point of this article with these expectations? Henry Delforn (talk) 04:59, 30 June 2009 (UTC)

+1 to this, my thoughts exactly. Thanks to this link for providing that information, which originally comes from Misner, Thorne, and Wheeler. 197.2.217.148 (talk) 00:04, 24 March 2017 (UTC)
As it says in the summary section, "Despite the use of partial derivatives, these equations are invariant under arbitrary curvilinear coordinate transformations. Thus if one replaced the partial derivatives with covariant derivatives, the extra terms thereby introduced would cancel out.". JRSpriggs (talk) 04:19, 24 March 2017 (UTC)