1998/10/31 by James W. York, James W. York, Jr · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Conformal geometry #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #Curvature #General relativity #Geometry #Hypersurface #Mathematical analysis #Mathematical physics #Mathematics #Mean curvature #Physics #Transformation (genetics) #gr-qc
paper · pdf · doi:10.1103/physrevlett.82.1350
published as Phys.Rev.Lett. 82 (1999) 1350-1353 · 7 pages, RevTeX
arxiv created 1998/12/23 · openalex publication_date 1999/02/15 · arxiv updated 2012/08/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
The initial-value problem is posed by giving a conformal three-metric on each of two nearby spacelike hypersurfaces, the proper-time separation of the hypersurfaces up to a multiplier to be determined, and the mean (extrinsic) curvature of one slice. The resulting equations have the same elliptic form as in the one-hypersurface formulation. The metrical roots of this form are revealed by a conformal ``thin sandwich'' viewpoint coupled with the transformation properties of the lapse function.