Unique continuation for the vacuum Einstein equations

2009/02/06 by Spyros Alexakis, Alexakis, Spyros · 4 citations
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.0902.1131

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.

Cited by

• Backwards uniqueness of the Ricci flow
• Ricci flow and the holonomy group
• An energy approach to the problem of uniqueness for the Ricci flow
• Rigidity of asymptotically conical shrinking gradient Ricci solitons

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