New General-Relativistic Thin-Sandwich Theorem

Publisher Website
Google Scholar
Abstract
Employing a new set of canonical variables for the gravitational field, the configuration variables are assigned on two infinitesimally neighboring spacelike hypersurfaces. It is shown that the problem of determining a solution of the vacuum Einstein field equations consistent with the given data can be reduced to a system of five elliptical differential equations. The determination of the Ricci-flat space-time is consequently reduced to a Dirichlet problem requiring data on a two-dimensional surface bounding a three-dimensional spacelike region.