GENERAL PHYSICS – GRAVITATION LOCAL SPACE-TIME TRANSLATION SYMMETRY?

A theory based on the gravitational gauge group is used in order to obtain a static solution of the field equations for the gravitational potentials. The gravitational gauge group and the corresponding gauge covariant derivative are introduced. The strength tensor of the gravitational gauge field is obtained and a gauge invariant Lagrangian is constructed. The field equations of the gauge potentials are written and a gravitational conserved current is determined. It is shown that the theory of the gravitational field based on the gravitational gauge group is equivalent to the General Relativity of Einstein. A model with gauge potentials depending only of spatial x coordinate is presented and its gauge field equations are written. An analytical solution of these equations is then determined. All the calculations are performed using a computer algebra package, running on the MapleV platform, along with several routines that we have written for our model. The integration of the field equation is also performed by this computer algebra package. 1