Lorentzian Metrics from Characteristic Surfaces

TL;DR

This paper investigates conditions under which families of hypersurfaces can serve as null surfaces of a Lorentzian metric, proposing a framework to use these surfaces as fundamental variables in General Relativity.

Contribution

It provides criteria for when hypersurface families define null surfaces of an unknown metric, enabling their use as fundamental variables in GR.

Findings

Conditions for hypersurface families to be null surfaces of a metric

Framework for using hypersurfaces as variables in GR

Potential for new approaches in gravitational theory

Abstract

The following issue is raised and discussed; when do families of foliations by hypersurfaces on a given four dimensional manifold become the null surfaces of some unknown, but to be determined, metric $g_{ab}(x)$? It follows from these results that one can use these surfaces as fundamental variables for GR.