On Strong Unique Continuation of Coupled Einstein Metrics

Willie Wai-Yeung Wong, Pin Yu
2012 International mathematics research notices  
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
more » ... man 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.
doi:10.1093/imrn/rnr038 fatcat:alpiywjzrrasdeqnjdquz64sv4