Knot points of a double-covariant system of elliptic equations and preferred frames in general relativity

摘要

We investigate the elliptic system of equations, which is general-covariant and locally SU(2)-covariant. For this system, we obtain the new condition of the Dirichlet problem solvability and the condition of the absence of zeroes for the solutions. This system contains, in particular, the Sen-Witten equation. On this basis, we prove the existence of the wide class of hypersurfaces, in all points of which there exists a correspondence between the Sen-Witten spinor field and three-frames, as well as preferred lapses and shifts. The Nester special orthonormal frame also exists on a certain subclass containing not just the maximal hypersurfaces. [References: 16]