Geometry of null hypersurfaces

TL;DR

This paper reviews the geometry of null hypersurfaces, focusing on their intrinsic objects, Gauss-Codazzi constraints, and applications to Bondi cones, providing a geometric framework for understanding null surfaces in general relativity.

Contribution

It introduces a tensor density framework for null hypersurfaces and applies it to analyze Bondi cones, advancing the geometric understanding of null surfaces.

Findings

Gauss-Codazzi constraints expressed via a tensor density

Introduction of a canonical ADM momentum analog for null surfaces

Analysis of Bondi cones using the new geometric objects

Abstract

We review some basic natural geometric objects on null hypersurfaces. Gauss-Codazzi constraints are given in terms of the analog of canonical ADM momentum which is a well defined tensor density on the null surface. Bondi cones are analyzed with the help of this object.