2000/01/31 by Michael T. Anderson
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Characterization (materials science) #Completeness (order theory) #Einstein #Einstein equations #Einstein field equations #General relativity #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Hypersurface #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Physics #Spacetime #Uniqueness #gr-qc #math.DG
paper · pdf · doi:10.1007/pl00001026
published as Annales Henri Poincare 1 (2000) 995 · 34 pages, Final version - contains corrections and improvements to initial version. Annales Henri Poincare, (to appear)
arxiv created 2000/10/29 · openalex publication_date 2000/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A complete characterization is obtained of the asymptotic behavior of solutions of the static vacuum Einstein equations which have a (pseudo)-compact horizon or boundary and are complete away from the boundary. It is proved that the time-symmetric space-like hypersurface has only finitely many ends, each of which is either asymptotically flat (AF) or parabolic, as in the (static) Kasner metric. Examples are given with both types of behavior, together with an extensive discussion and new characterization of Weyl metrics. The asymptotics result allows one in most circumstances to drop the AF assumption from the static black hole uniqueness theorems and replace it with just a completeness assumption.