An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity

TL;DR

This paper provides an introduction to conformal geometry and tractor calculus, emphasizing their applications in general relativity, including conformally invariant tensors, differential operators, and conformally compactified geometries.

Contribution

It offers an accessible overview of conformal tractor calculus and demonstrates its relevance to problems in general relativity, especially in understanding conformal infinity.

Findings

Development of conformal tractor calculus framework

Application to conformally compactified geometries

Insights into conformal invariance in general relativity

Abstract

The following are expanded lecture notes for the course of eight one hour lectures given by the second author at the 2014 summer school Asymptotic Analysis in General Relativity held in Grenoble by the Institut Fourier. The first four lectures deal with conformal geometry and the conformal tractor calculus, taking as primary motivation the search for conformally invariant tensors and diffrerential operators. The final four lectures apply the conformal tractor calculus to the study of conformally compactified geometries, motivated by the conformal treatment of infinity in general relativity.