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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 different proof of that result using a Carleman inequality (and thus circumventing the use of analyticity). Hence the method is robust under certain nonanalytic perturbations. As an example, we also show the strong unique continuation property for the Riemannian Einstein-scalar-field system with cosmological constant.

On Strong Unique Continuation of Coupled Einstein Metrics