In this link, I have learned how to solve Einstein equation in 4 dimensional spacetime, but how to solve it in general dimension? For example, in $(n+1)$ dimensional spacetime, the metric is

$$ \frac{d s^2}{l^2}=\frac{d v^2}{v^2 f(v)}+\frac{1}{v^2}\left(-f(v) d t^2+d z^2+\delta_{i j} d x^i d x^j+h_{\alpha \beta}(v) e^{i k z} d x^\alpha d x^\beta\right) $$

where $i,j=1,\cdots,n-2$, $\alpha,\beta=1,\cdots,n$, Einstein's equation in AdS spacetime is

$$ 0 = R_{a b} - \frac{1}{2}R_{c d} g^{c d} g_{a b} - \frac{n\left(n-1\right) }{2 {l}^2}g_{a b} $$

where $l$ is the AdS radius. How to obtain the components of Einstein's equation?