Seminarium Teorii Względności i Grawitacji

The Fefferman-Graham obstruction tensor is an interesting conformal invariant, which vanishes on solutions of Einstein's equations. It is a complicated object and it depends on high order derivatives of the metric. However, it shares many nice properties of the Einstein tensor. In particular, it has a well-posed initial value problem ( it is hyperbolic in a suitable gauge). Due to conformal properties, vanishing of the obstruction tensor can serve as a useful tool for analyzing asymptotic behaviour of solutions of the Einstein field equations.