I'm considering a metric of the following form (signature $(+,-,-,-)$): $$ds^2 = (F(r,t)-G(r,t))dt^2 - (F(r,t)+G(r,t))dr^2 - r^2(d\Omega)^2$$
where $F(r,t)$ and $G(r,t)$ are arbitrary scalar functions.
I am trying to find a coordinate and/or conformal transformation to one of the 'standard' Robertson-Walker forms, e.g.
$$ds^2 = dT^2 - a(T)^2/(1-kR^2)dR^2 - R^2(d\Omega)^2$$
for any $k=0,-1,+1$, or show that there isn't one.