Energy problem in the Einstein–Cartan theory

Abstract

The Einstein–Cartan–Kibble–Sciama equations are presented in the following form: the codifferential of the differential of a tetrad is the tetrad current with the ordinary conservation law. This form is an analogue of the form for non-Abelian quantum field theory. A canonical gauge tetrad is proposed for six two-directions with extreme sectional Riemannian curvature. A nonlocal conservation law for the contracted Bianchi identities is presented. The physical and geometric meaning of the Gibbons-Hawking Lagrangian and surface term are proposed. Application of the tetrad current concept is illustrated for the Schwarzschild and de Sitter metrics.