Dipole gravitational radiation in the nonsymmetric gravitational theory of Moffat

The generation of gravitational radiation in the nonsymmetric gravitational theory (NGT) of Moffat is analyzed. It is shown that the theory predicts the emission of dipole gravitational radiation from a binary system. The source of the dipole radiation is a vector density S postulated to be proportional to the number density of fermion particles in the components of the system. This radiation is shown to result in a secular decrease in the orbital period of a binary system in addition to that predicted by general relativity. The size of the effect is proportional to the reduced mass of the system and to the square of the difference in $l^2$/[mass] between the two components of the system, where l is a parameter having units of [length] that is related to the number of fermion particles in each component. As part of the analysis, the stress-energy pseudotensor of the NGT, expanded to quadratic order in the gravitational fields, and the NGT gravitational-wave luminosity formula are derived for the first time. With a perfect-fluid model of matter, results are also given for the post-Newtonian expansions of the source densities of the gravitational fields. The results of this analysis are then applied to the binary pulsar system PSR 1913+16 which contains a pulsar orbiting an unobserved companion. With gravitational radiation attributed as the cause of the observed secular decrease in the orbital period, this system provides a test of the prediction by the NGT of dipole gravitational radiation. It is shown that the NGT can only fit the observations of this system provided the l parameter of the unseen companion is ≲350 km.