Desitter Gauge Theory Of Gravitation

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation.Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor$(F_{\mu\nu}^a, F_{\mu\nu}^{ab})$, Riemann tensor$\tilde R_{\mu\nu}^{\rho\sigma} =R_{\mu\nu}^{ab} e_a^\rho e_b^\sigma$, Ricci tensor$\tilde R_\mu^\nu$, curvature scalar$\tilde R$, field equations, and the integration of these equations.