The linearised Einstein equations as a gauge theory

TL;DR

This paper reformulates the linearised Einstein vacuum equations with a cosmological constant using the Calabi operator from projective differential geometry, providing a new geometric perspective.

Contribution

It introduces a novel approach to linearising Einstein's equations through the Calabi operator, bridging differential geometry and general relativity.

Findings

Reformulation of Einstein equations using the Calabi operator

Establishment of a geometric framework for linearised gravity

Potential implications for understanding gravitational perturbations

Abstract

We linearise the Einstein vacuum equations with a cosmological constant via the Calabi operator from projective differential geometry.