Gravitational field equations coupled with the U(1)xSU(2) and U(1)xU(1)xSU(2) gauge fields

Abstract

The SL(2,C) × U(1) × SU(2) gauge group is chosen for the gauge theory of Einstein, Maxwell, and Yang-Mills fields. From this model, the coupled field equations are obtained, and then, using the Newman-Penrose formalism, the gravitational field equations including the effect of Maxwell and Yang-Mills fields are obtained. The ideas used here are extended by allowing for the presence of magnetic monopoles. The extension of the SL(2,C) × U(1) × SU(2) is performed by enlarging the gauge group to the SL(2,C) × U(1) × U(1) × SU(2). In this research, the U(1) effects on the matter-free gravitation are found to be equivalent to the U(1) × U(1).