Abstract:
In the usual construction of conformal tractor calculus on a pseudo-Riemannian manifold, there is an assumption of nondegeneracy of the metric. So if we were to lift this assumption, we would need to redefine the tractor machinery. This is of particular interest in the study of the asymptotics of space-times, which have metrics that are not positive-definite. These space-times are often modelled as compactified manifolds, with boundary I , referred to as null-infinity, which has the structure of a conformal manifold with a degenerate direction. Then if we want to study conformally invariant objects on I , we are inclined to develop this new tractor calculus. This is done in [13]. with the motivation of modelling the geometry of gravitational waves. We aim to adapt this definition into a more familiar setting by studying the Minkowski case and defining tractor machinery in relation to the ambient tractor bundle.
