Reference: Moore, Thomas A., *A General Relativity Workbook*, University Science Books (2013) – Chapter 6; Problem 6.10, 7.2.

The electromagnetic field tensor* * is

The various electromagnetic laws can be expressed by the equation

The lowered version of in the flat metric of special relativity is

Because , if we set two of the indices equal in this equation, the LHS is identically zero. For example if :

Since the three terms are cyclic permutations of each other, setting any other pair of indices equal gives the same result.

If we choose , , , we get

This is the law .

If we now choose , , , we get

This is the component of Faraday’s law .

Other choices give the remaining components of Faraday’s law.

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