- #1
jstrunk
- 55
- 2
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 don't 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 don't 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?