A Conformal Extension Theorem based on Null Conformal Geodesics

TL;DR

This paper introduces a conformal extension theorem utilizing null conformal geodesics and tractor formalism, providing conditions for extending spacetime through isotropic singularities.

Contribution

It formulates null geodesics as null conformal geodesics within tractor formalism and proves a conformal extension theorem based on curvature boundedness.

Findings

Proves a conformal extension theorem through isotropic singularities.

Describes null geodesics as null conformal geodesics in tractor formalism.

Extends earlier work by Tod and Luebbe.

Abstract

In this article we describe the formulation of null geodesics as null conformal geodesics and their description in the tractor formalism. A conformal extension theorem through an isotropic singularity is proven by requiring the boundedness of the tractor curvature and its derivatives to sufficient order along a congruence of null conformal geodesic. This article extends earlier work by Tod and Luebbe.