Equivalence principle in the new general relativity

Takeshi Shirafuji, Saitama University
Gamal G.L. Nashed, Saitama University
Yoshimitsu Kobayashi, Saitama University


We study the problem of whether the active gravitational mass of an isolated system is equal to the total energy in the tetrad theory of gravitation. The superpotential is derived using the gravitational Lagrangian which is invariant under the parity operation and applied to an exact spherically symmetric solution. Its associated energy is found to be equal to the gravitational mass. The field equation in vacuum is also solved at far distances under the assumption of spherical symmetry. Using the most general expression for parallel vector fields with spherical symmetry, we find that the equality of the gravitational mass and the energy always holds if the parameters of the theory a1, a2 and a3 satisfy the condition (a1 + a2)(a1 - 4a3/9) ≠ 0. In the two special cases where either (a1 + a2) or (a1 - 4a3/9) is vanishing, however, this equality is not satisfied for the solutions when some components of the parallel vector fields tend to zero as 1/√r for large r.