Journal Article

Equivalence Principle in the New General Relativity

Takeshi Shirafuji, Gamal G.L. Nashed and Yoshimitsu Kobayashi

in Progress of Theoretical Physics

Published on behalf of The Physical Society of Japan

Volume 96, issue 5, pages 933-947
Published in print November 1996 | ISSN: 0033-068X
Published online November 1996 | e-ISSN: 1347-4081 | DOI: http://dx.doi.org/10.1143/PTP.96.933
Equivalence Principle in the New General Relativity

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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.

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