An extension theorem for conformal gauge singularities

TL;DR

This paper investigates conditions under which conformal gauge singularities in cosmological models can be locally extended through using tractor calculus, providing a new mathematical framework for understanding singularities in general relativity.

Contribution

It introduces a tractor calculus-based method to determine when conformal structures can be extended through singularities, offering a novel mathematical approach.

Findings

Derived conditions for local extension of conformal structures

Proved a local extension theorem for conformal gauge singularities

Applied tractor curvature analysis to cosmological singularities

Abstract

We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem.