Time (in)dependence in general relativity

1. Nov 30, 2013

benjamin_cro

Hello,

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

Thanks,
Benjamin

2. Nov 30, 2013

Bill_K

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.