Exact Results in Quantum Theory & Gravity

The Fefferman-Graham obstruction tensor is an interesting conformal invariant, which vanishes on solutions of Einstein's equations. Although it is complicated and depends on high derivatives of the metric, it also shares many nice properties of the Einstein tensor. In particular, vanishing of the obstruction tensor has a well-posed initial value problem (it is hyperbolic in a suitable gauge). Due to conformal properties, this equation can serve as a useful tool for analyzing asymptotic behaviour of solutions of the Einstein field equations. The proof of hyperbolicity is not trivial and it involves ambient metric construction of Fefferman and Graham.