Equivalence principle in the new general relativity

Details Equivalence principle in the new general relativity Equivalence principle in the new general relativity

1996-09-26

arxiv.org/abs/gr-qc/9609060v1

Prog.Theor.Phys. 96 (1996) 933-948

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, LaTeX, published in Prog. Theor. Phys. 96 No.5 (1996)

Scientific paper

10.1143/PTP.96.933

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 parity operation, and applied to an exact spherically symmetric solution. Its associated energy is found 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 between the gravitational mass and the energy is always true if the parameters of the theory $a_1$, $a_2$ and $a_3$ satisfy the condition, $(a_1+ a_2) (a_1-4a_3/9)\neq0$. In the two special cases where either $(a_1+a_2)$ or $(a_1-4a_3/9)$ is vanishing, however, this equality is not satisfied for the solutions when some components of the parallel vector fields tend to zero as $1/\sqrt{r}$ for large $r$.

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