Some hints for special case of metric tensor in GR

Question

Let's have metric $$ ds^2 = dt^2 - dx^2 - dy^2 - dz^2 - 2f(t - z, x, y)(dt - dz)^2. $$ I need to prove that it is an exact solution for Einstein equations in vacuum for $\partial_{x}^{2}f + \partial_{y}^{2}f = 0$.

The straightforward method is obvious, but does some method especially for this metric exist?

Edit. As I see, first is replacing the variables as $$ u = (t - z), \quad v = (t + z). $$

This post imported from StackExchange Physics at 2014-03-05 14:55 (UCT), posted by SE-user Andrew McAddams