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

TL;DR

This paper investigates a general-covariant elliptic system in general relativity, establishing conditions for solvability and zeros absence, and demonstrating the existence of hypersurfaces with special frame-spinor correspondences.

Contribution

It introduces new solvability and zeros conditions for a covariant elliptic system, extending the understanding of frame-spinor relations in general relativity.

Findings

Existence of solutions under new Dirichlet conditions

Identification of hypersurfaces with frame-spinor correspondence

Generalization of Nester orthoframe beyond maximal hypersurfaces

Abstract

The elliptic system of equations, which is general-covariant and locally SU(2)-covariant, is investigated. The new condition of the Dirichlet problem solvability and the condition of zeros absence for solutions are obtained for this system, which contains in particular case the Sen-Witten equation. On this basis it is proved 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-frame, which generalizes the Nester orthoframe. The Nester special orthoframe also exists on a certain subclass containing not only the maximal hypersurfaces.