Conformal tractor calculus for static and stationary spacetimes

Abstract

We present a new approach to stationary and static spacetimes using the conformal tractor calculus. In this approach the natural prolongations of the conformal Einstein equation and the conformal Killing equation in terms of tractor calculus play a central role. In order to present tractor calculus for stationary and static spacetimes we have given a significant amount of background material on basic differential geometry, pseudo-Riemannian and conformal geometry, stationary and static spacetimes, and conformal tractor calculus. We also give new and fundamental results on Lie derivatives of conformal tractor fields with respect to conformal Killing vector fields.