Plane-fronted gravitational wave

For

d s^{2} = 2 d u d v + d x^{2} + d y^{2} + H (u, x, y) d u^{2},

the only potentially nonzero Ricci component is

R_{uu} = - \frac{1}{2} (H_{xx} + H_{yy}) .

The vacuum equation is therefore the transverse Laplace equation.

 Ancestors (4)