Pelykh V. Local covariant methods and the positive energy problem in general relativity

Differential geometry of the spinor fields, associated with hyperdistributions, and a method for description of interaction between spinorial and gravity-inertial fields have been developed. A method for investigation of the node manifolds of double-covariant systems of elliptic equations has been elaborated, and the tensor method for proving the theorem about the positive gravitation energy on nonmaximal hypersurfaces has been developed on this basis. The ADM method for problem of the gravitation energy quasi-localization has been generalized for the systems with radiation; connections between the local triad method for the gravitation energy quasilocalization and the method of the 4-covariant spinorial Nester’s 3-form have been established. Positivity of gravitation energy on asymptotically flat manifolds has been proven.