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## Main Question or Discussion Point

The General Relativity text I am using gives two forms of the Electromagnetic Energy Momentum Tensor:

[tex]{\rm{ }}\mu _0 S_{ij} = F_{ik} F_{jk} - \frac{1}{4}\delta _{ij} F_{kl} F_{kl} \\[/tex]

[tex]{\rm{ }}\mu _0 S_j^i = F^{ik} F_{jk} - \frac{1}{4}\delta _{ij} F^{kl} F_{kl} \\[/tex]

I dont see how these are equivalent. Raising one index on the left entitles you to raise one index on

each term on the right, but instead they raised two indexes on the right. Can anyone explain this?

[tex]{\rm{ }}\mu _0 S_{ij} = F_{ik} F_{jk} - \frac{1}{4}\delta _{ij} F_{kl} F_{kl} \\[/tex]

[tex]{\rm{ }}\mu _0 S_j^i = F^{ik} F_{jk} - \frac{1}{4}\delta _{ij} F^{kl} F_{kl} \\[/tex]

I dont see how these are equivalent. Raising one index on the left entitles you to raise one index on

each term on the right, but instead they raised two indexes on the right. Can anyone explain this?