JUNCTION CONDITIONS FOR NULL BOUNDARIES IN ADMISSIBLE COORDINATES

Abstract

Normal Gaussian prescription breaks down when treating null boundaries since the normal to a null boundary declines into tangency to the boundary. The normal extrinsic curvature is therefore disabled as a carrier of transverse geometrical information for a null boundary. In this paper we will construct a distributional approach based on admissible coordinates to find junction conditions and dynamics of null boundaries. Since a general null boundary can consist of matter and stress-energy distribution, we consider the general case of a null "shell" or "boundary layer". As a simple example, junction conditions and dynamics of a spherical null shell with non-vanishing energy–momentum content are derived.