Colliding Impulsive Gravitational Waves and a Cosmological Constant

TL;DR

This paper models the collision of two impulsive gravitational waves in a space-time with a cosmological constant, deriving the post-collision space-time with constant curvature and relating the cosmological constant to the wave profiles.

Contribution

It introduces a new exact solution describing colliding impulsive gravitational waves with a cosmological constant, linking wave profiles to the resulting space-time curvature.

Findings

Post-collision space-time has constant curvature.

Cosmological constant is determined by wave profiles as =-6kl.

Provides a mathematical model for wave collision in curved space-time.

Abstract

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 $\Lambda=-6\,k\,l$.