Projective differential geometry and asymptotic analysis in General Relativity

TL;DR

This paper develops a projective exterior differential tractor calculus for asymptotic analysis of classical fields on projectively compact manifolds, extending tools from differential geometry to general relativity contexts.

Contribution

It introduces a novel tractor calculus for projectively compact manifolds, analogous to conformal cases, aiding asymptotic analysis in general relativity.

Findings

Developed a projective exterior differential tractor calculus.

Extended differential geometric tools to projectively compact manifolds.

Facilitated asymptotic analysis of classical fields in general relativity.

Abstract

In this text, we explore the tools that Projective Differential Geometry can provide for the asymptotic analysis of classical fields on projectively compact manifolds. We emphasise on the case of order 2-compactifications and develop, in this case, a projective exterior differential tractor calculus that is analogous to that existing for conformally compact manifolds.