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 $u=0, v=0$ are intersecting null hypersurfaces. The cosmological constant $\Lambda$ in the post collision region of the space--time is given by $\Lambda=-6\,k\,l$.