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Varying metric determinant

  1. Jan 15, 2006 #1
    Let h = det h_{alpha beta}. The number of dimensions is not necessarily four. Show that
    [tex]
    \[
    \delta h = -h h_{\alpha \beta} \delta h^{\alpha \beta} \, ;
    \]
    [/tex]

    delta h is the variation in h.

    Not sure how to start.
     
  2. jcsd
  3. Jan 16, 2006 #2

    dextercioby

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    Science Advisor
    Homework Helper

    HINT:

    [tex] \mbox{det} A=\exp\mbox{Tr} \ \ln A [/tex]

    Daniel.
     
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