A computer aided study of de-Sitter gauge theory of gravitation

A gauge theory for gravitation is constructed with the de-Sitter group as structural group and having a Minkowski space–time in spherical coordinates as base manifold. It is supposed that the gravitational field is created by a point-like source of mass mm that also has an electrical charge QQ. The strength tensors of the gravitational gauge fields are calculated and the field equations are obtained using the energy–momentum tensor for the electromagnetic field. The solutions of these equations are also studied. It is shown that one of the solutions includes simultaneously the Schwarzschild, Reissner–Nordström and de-Sitter metrics. All the calculations, including the integration of the field equations, have been performed using an analytical program written by us in the package GRTensorII. The program can be applied to any gauge theory having both space–time and internal local symmetries.