  The strong unique continuation property for Einstein metrics can be concluded
from the well-known fact that Einstein metrics are analytic in geodesic normal
coordinates. Here we give a proof of the same result that given two Einstein
metrics with the same Ricci curvature on a fixed manifold, if they agree to
infinite order around a point, then they must coincide, up to a local
diffeomorphism, in a neighborhood of the point. The novelty of our method lies
in the use of a Carleman inequality and thus circumventing the use of
analyticity; thus the method is robust under certain non-analytic
perturbations. As an example, we also show the strong unique continuation
property for the Riemannian Einstein-scalar-field system with cosmological
constant.
