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arXiv · 0904.0465

On strong unique continuation of coupled Einstein metrics

Willie Wai-Yeung Wong·Pin Yu
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Abstract

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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Willie Wai-Yeung Wong, Pin Yu. 2009-09-23. On strong unique continuation of coupled Einstein metrics. https://doi.org/10.1093/imrn%2Frnr038

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