Unique continuation for the vacuum Einstein equations

Abstract

We derive a unique continuation theorem for the vacuum Einstein equations. Our method of proof utilizes Carleman estimates (most importantly one obtained recently by Ionescu and Klainerman), but also relies strongly on certain geometric gauge constructions which make it possible to address this problem via such estimates. We indicate how our method can be used more broadly to derive unique continuation for Einstein's equations from Carleman estimates for the wave operator.

updated version

References in corpus (2)

• On the uniqueness of smooth, stationary black holes in vacuum
• Continuation unique a partir de l'infini conforme pour les metriques d'Einstein

Cited by in corpus (7)

• Laplacian flow for closed G_2 structures: Shi-type estimates, uniqueness and compactness
• On strong unique continuation of coupled Einstein metrics
• Backwards uniqueness of the Ricci flow
• Rigidity of asymptotically conical shrinking gradient Ricci solitons
• Hawking's local rigidity theorem without analyticity
• An energy approach to the problem of uniqueness for the Ricci flow
• Ricci flow and the holonomy group