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 $k\,δ(u)$ and $l\,δ(v)$ where $k, l$ are real constants and $u=0, v=0$ are intersecting null hypersurfaces. The cosmological constant $Λ$ in the post collision region of the space--time is given by $Λ=-6\,k\,l$.

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