- #1
shooride
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I read in many books the metric tensor is rank (0,2), its inverse is (2,0) and has some property such as
##g^{\mu\nu}g_{\nu\sigma}=\delta^\mu_\sigma## etc. My question is: what does ##g^\mu_\nu## mean?! This tensor really confuses me! At first, I simply thought that ##g^{\mu\nu}\delta_{\mu\sigma}=g^\nu_\sigma##, but I realized it is not true. Is ##g^\mu_\nu## a metric, again? I mean can I write something like ##g^\mu_\nu x^\nu=x^\mu##?
##g^{\mu\nu}g_{\nu\sigma}=\delta^\mu_\sigma## etc. My question is: what does ##g^\mu_\nu## mean?! This tensor really confuses me! At first, I simply thought that ##g^{\mu\nu}\delta_{\mu\sigma}=g^\nu_\sigma##, but I realized it is not true. Is ##g^\mu_\nu## a metric, again? I mean can I write something like ##g^\mu_\nu x^\nu=x^\mu##?
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