The Sandwich Conjecture

Abstract

The “Sandwich Conjectyre” (SC) was originally formulated by Wheeler and his coworkers.¹ In the course of several years both the original author(s) and others have proposed the statement in several different forms, and with different qualifications. Roughly, the SC asserts that in a purely gravitational field the internal geometries of two distinct three-dimensional space-like hypersurfaces determine uniquely the geometry of a four-dimensional space-time (i.e. pseudo-Riemannian) manifold that is required to obey Einstein’s field equations (i.e. to be Ricci-flat). In a careful formulation one will have to specify further whether the two three-surfaces are to be “close together”, whether the distance between them is to be given as additional data, and what sort of conditions are to be imposed at space-like infinity.

Research supported in part by ARL and by AFOSR.