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$$ds^2 = e^{v}dt^2 - e^{u}dr^2 - r^2(d\theta^2 +sin^2\theta d\phi^2)$$

where v and u are functions of r only

when we calculate the Ricci tensor $R_{\mu\nu}$ the non vanishing ones will only be $$R_{tt}$$,$$R_{rr}$$, $$R_{\theta\theta}$$,$$R_{\phi\phi}$$

But when u and v now depend on r and t, we get an extra term of Ricci tensor which is the

$$R_{tr}$$ I thought that if our matrix is diagonal we should not get a non diagonal Ricci tensor and all the Ricci tensors must be diagonal. Am I mistaken?