Gravitational Waves with Colliding or Non--Colliding Wave Fronts

TL;DR

This paper introduces a scheme to analyze whether wave fronts in gravitational radiation models, described by Einstein's vacuum equations, collide or not, by examining the intersection of null hypersurfaces.

Contribution

It provides a method to explicitly determine the collision or non-collision of wave fronts in exact solutions of Einstein's equations.

Findings

Scheme effectively identifies intersecting wave fronts.

Distinguishes between colliding and non-colliding wave fronts.

Applicable to known exact solutions of gravitational radiation.

Abstract

The known exact solutions of Einstein's vacuum field equations modeling the gravitational fields of pure gravitational radiation involve wave fronts which are either planar or roughly spherical. We describe a scheme designed to check explicitly whether or not the wave fronts collide. From the spacetime point of view the scheme determines whether or not the null hypersurface histories of the wave fronts intersect and, in particular, allows easy identification of the cases in which the null hypersurfaces do not intersect.