2021/08/18 by Wojciech Kamiński, Kamiński, Wojciech · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2108.08085
openalex publication_date 2021/08/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Vanishing of the Fefferman-Graham obstruction tensor was used by Andersson and Chruściel to show stability of the asymptotically de Sitter spaces in even dimensions. However, existing proofs of hyperbolicity of this equation contain gaps. We show in this paper that it is indeed a well-posed hyperbolic system with unique up to diffeomorphism and conformal transformations smooth development for smooth Cauchy data. Our method applies also to equations defined by various versions Graham-Jenne-Mason-Sparling operators. In particular, we use one of these operators to propagate Gover's condition of being almost conformally Einstein. This allows to study initial data also for Cauchy surfaces which cross conformal boundary. As a by-product we show that on globally hyperbolic manifolds one can always choose conformal factor such that Branson Q-curvature vanishes.