I keep coming across calculations like this,
Consider a metric on an $n+2$ dimensional manifold given as,
$ds^2 = 2dudr + 2L(u,r)du^2 -r^2d\Omega_n^2$
Then apparently once can write down the Ricci and Einstein and other tensors as a function of n.
Like for the above the Einstein tensor apparently has the following non-zero components,
$G_{01} = \frac{n}{r}L_r+\frac{n(n-1)(2L-1)}{2r^2}$
$G_{22} = (n-1)[(2L-1)(\frac{2-n}{2})-2rL_r]-r^2L_{rr}$
$G_{00} = -\frac{nL_u}{r} + \frac{2nLL_r}{r} + \frac{n(n-1)L(2L-1)}{r^2}$
and $G^2_2 = G^3_3 = ... = G^{n+1}_{n+1}$
(where the subscripts of L denote partial derivatives with respect to those variables)
For a fixed given n I can imagine doing the calculation either by hand or some software but I would like to know who these expressions are derived for a general n.