Time-Indep General Relativity: Can Someone Help Understand Equation (10)?

[benjamin_cro]

Hello,

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.

Thanks,
Benjamin

 

[Bill_K]

A spherically symmetric tensor can only contain two terms: a scalar times δ_ij, 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 ∂_i∂_jB(r) is, and you'll find that it also involves only terms of the same kind: δ_ij and $\hat{r_i} \hat{r_j}$. So the two forms of the tensor are equivalent.