On strong unique continuation of coupled Einstein metrics

Details On strong unique continuation of coupled Einstein metrics On strong unique continuation of coupled Einstein metrics

2009-04-02

arxiv.org/abs/0904.0465v2

Mathematics

Analysis of PDEs

12 pages; some minor errors are fixed in revision, some clarifications are made

Scientific paper

10.1093/imrn/rnr038

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.

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