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Covariant conservation

  1. Sep 20, 2012 #1
    suppose we have unit vector z=(0,0,0,1), we can use it to form a tensor [itex]z^\mu z^\nu [/itex],
    it is easy to check that [itex]∂_\μ( z^\mu z^\nu[/itex]=0 in Minkowski spacetime,
    now I want to generalize this equation to general curved spacetime, so that
    ∇μ ([itex] znew^\mu znew^\nu[/itex])=0.
    But I am not sure how to find znew, which should be related to the original z.
    Any one can help me? Thanks
    Last edited: Sep 21, 2012
  2. jcsd
  3. Sep 20, 2012 #2


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    Welcome to PF! Could you please mark up your equations using LaTeX so they're more readable? Here's an example: [itex]z^\mu[/itex]. To see how I did this, click on the QUOTE button underneath mypost.
  4. Sep 21, 2012 #3
    each time when I tried to submit the revision, the web kept saying it is too short, need to lengthen it to at least 4 characters, i do not know what does that mean.
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