Colliding Impulsive Gravitational Waves and a Cosmological Constant

We present a space–time model of the collision of two homogeneous, plane impulsive gravitational waves (each having a delta function profile) propagating in a vacuum before collision and for which the post collision space–time has constant curvature. The profiles of the incoming waves are $k\delta (u)$ and $l\delta (v)$ where $k,l$ are real constants and $u=0, v=0$areintersectingnullhypersurfaces\mathrm{.}Thecosmologicalconstant$\Lambda$inthepostcollisionregionofthespace--timeisgivenby$\Lambda=-6,k,l$.