(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I attach a word document with the equations because I dont know how to write them on the post.

My question reads: Show that Maxwell's equations Eq (1) is equivalent to Eq (3).

2. Relevant equations

The first term of Eq 1 reads: F sub alpha beta comma gamma. That means partial of F sub alpha beta with respect to x super gamma.

The book says that Eq 1 and Eq 2 are equivalents. I am just showing Eq 2 because I know that the book's notation is confusing.

Eq 2 means the gradient of F, which is the EM tensor.

Eq (4) is the components electromagnetic tensor.

And I have calculated the components of the dual tensor *F which are Eq (5)

3. The attempt at a solution

I have written Eq (3) in matrix notation, but I dont think it resembles Eq (1) or Eq (2). Also, I know that Eq 2 is a 3rd rank tensor due to the gradient.

I have no idea how to show the equivalency between 1 and 3.

The book Im using is Mister, Thorne, Wheeler Gravitation, but this is a undergraduate level course in general relativity, and I am very new at this tensor stuff, so please be gently.

Thank you for your help

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# Electromagnetic dual tensor. General Relativity

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