Configurations with a vector field in the Einstein-Cartan theory

The properties of self-gravitating distributions of an ideal fluid charged by a vector field which is either massive or massless, i.e., electromagnetic, are considered taking account of the spin properties of the vector field in the framework of the Einstein-Cartan theory of gravitation. Conditions for equilibrium are found and the corresponding exact solutions are obtained. A complete system of first integrals of the corresponding equations of motion is found for dynamical distributions in the absence of pressure. A theorem on the correspondence between the dynamics of an electrically charged ideal fluid with a limiting equation of state and the dynamics of a free massive vector field is also proved.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 7–11, August, 1979.