Consistency of the Nonsymmetric Gravitational Theory

Abstract

The NGT field equations with sources are expanded first about a flat Minkowski background and then about a GR background to first-order in the antisymmetric part of the fundamental tensor, $g_{μν}$. From the general, static spherically symmetric solution of the field equation in empty space, we establish that there are two conserved charges $m$ and $\ell^2$ corresponding to the two basic gauge invariances of NGT. There is no direct contribution to the flux of gravitational waves from the antisymmetric, $g_{[μν]}$, sector in the linearized, lowest order of approximation, nor in the non-linear theory. It is demonstrated that the flux of gravitational waves is finite in magnitude and positive definite for solutions of the field equations which satisfy the boundary condition of asymptotic flatness.