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Time (in)dependence in general relativity

  1. Nov 30, 2013 #1

    Can someone please help me to understand equation (10) from this article http://arxiv.org/abs/gr-qc/0607020.

    I do not see how does spherically symmetric tensor must (can) be written in that form.

  2. jcsd
  3. Nov 30, 2013 #2


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    A spherically symmetric tensor can only contain two terms: a scalar times δij, and a scalar times ## \hat{r_i} \hat{r_j} ##, where ## \hat{r_i} ## is the unit vector in the radial direction.

    Work out what ∂ijB(r) is, and you'll find that it also involves only terms of the same kind: δij and ## \hat{r_i} \hat{r_j} ##. So the two forms of the tensor are equivalent.
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