ENERGY AND MOMENTUM IN THE TETRAD THEORY OF GRAVITATION

We study the energy and momentum of an isolated system in the tetrad t heory of gravitation, starting from the most general Lagrangian quadra tic in torsion, which involves four unknown parameters. When applied t o the static spherically symmetric case, the parallel vector fields ta ke a diagonal form, and the field equation has an exact solution. We a nalyze the linearized field equation in vacuum at distances far from t he isolated system without assuming any symmetry property of the syste m. The linearized equation is a set of coupled equations for a symmetr ic and skew-symmetric tensor fields, but it is possible to solve it up to O(1/r) for the stationary case. It is found that the general solut ion contains two constants, one being the gravitational mass of the so urce and the other a constant vector B-alpha. The total energy is calc ulated from this solution and is found to be equal to the gravitationa l mass of the source. We also calculate the spatial momentum and find that its value coincides with the constant vector B-alpha. The lineari zed field equation in vacuum, which is valid at distances far from the source, does not give any information about whether the constant vect or B-alpha is vanishing or not. For a weakly gravitating source for wh ich the held is weak everywhere, we find that the constant vector B-al pha vanishes.