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Put $u=t-z$. Wherever $|u|>U$, the profile $A(u)$ vanishes and the displayed metric is exactly the Minkowski metric. Thus the two flat regions in the $(t,z)$-plane are the half-planes $t-z>U$ and $t-z<-U$, separated by the stripAt fixed $t$ this strip is $t-U\le z\le t+U$, so it has longitudinal width $2U$. A surface $u=\text{constant}$ obeys $z=t-u$ and travels in the positive $z$ direction at the speed of light. The curvature is confined to that moving strip, identifying the solution as a gravitational-wave pulse represented by a plane-fronted gravitational wave.

For the given metric, direct substitution of the stated connection coefficients into the curvature formula leavesThe inverse metric has $g^{uu}=0$, and every other Ricci component vanishes, soThus the full, nonlinear vacuum Einstein equation is precisely the transverse Laplace equation from a plane-fronted gravitational wave:The dependence on $u$ is unrestricted.