- #1
dm4b
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This is from Linearized Gravity in General Relativity, where h is the perturbation on the background Minkowski metyric.
Is the following valid?
[tex]\partial^{\sigma}h_{\sigma}_{\mu}=\eta^{\sigma}^{\epsilon}\partial_{\epsilon}h_{\sigma}_{\mu}=\partial_{\epsilon}h_{\mu}^{\epsilon}=\partial_{\sigma}h_{\mu}^{\sigma}[/tex]
As you can see on the third term, I use the metric (neta) to raise an index on h instead of the partial now. Is that valid?
Since the metric is full of constants in the Minkowski metric, seems like it would be valid to move it inside the partial and operate on h. BUT, seems like this would not be true in general, maybe?
Is the following valid?
[tex]\partial^{\sigma}h_{\sigma}_{\mu}=\eta^{\sigma}^{\epsilon}\partial_{\epsilon}h_{\sigma}_{\mu}=\partial_{\epsilon}h_{\mu}^{\epsilon}=\partial_{\sigma}h_{\mu}^{\sigma}[/tex]
As you can see on the third term, I use the metric (neta) to raise an index on h instead of the partial now. Is that valid?
Since the metric is full of constants in the Minkowski metric, seems like it would be valid to move it inside the partial and operate on h. BUT, seems like this would not be true in general, maybe?
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