Let's have metric
ds2=dt2−dx2−dy2−dz2−2f(t−z,x,y)(dt−dz)2.
I need to prove that it is an exact solution for Einstein equations in vacuum for
∂2xf+∂2yf=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),v=(t+z).
This post imported from StackExchange Physics at 2014-03-05 14:55 (UCT), posted by SE-user Andrew McAddams