Principal null directions of perturbed black holes

The properties of principal null directions of a perturbed black hole are investigated. It is shown that principal null directions are directly observable quantities characterizing the spacetime. A definition of a perturbed spacetime, generalizing that given by Stewart and Walker, is proposed. This more general framework allows one to include descriptions of a given spacetime other than by a pair (M, g) where M is a four-dimensional differential manifold and g a Lorentz metric. Examples of alternative characterizations are the curvature representation of Karlhede and others, the Newman–Penrose representation or observable quantities involving principal null directions. The conditions are studied under which the various alternative choices of observables provide equivalent descriptions of the spacetime.