Conformal “Thin-Sandwich” Data for the Initial-Value Problem of General Relativity

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Abstract
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.