Consistency of the Nonsymmetric Gravitational Theory

TL;DR

This paper analyzes the consistency of the Nonsymmetric Gravitational Theory (NGT) by expanding its equations around flat and GR backgrounds, identifying conserved charges, and examining gravitational wave flux properties.

Contribution

It provides a first-order expansion of NGT equations, identifies conserved charges, and demonstrates the positivity and finiteness of gravitational wave flux in NGT.

Findings

Two conserved charges m and ℓ² identified in NGT.

No direct gravitational wave flux contribution from the antisymmetric sector.

Gravitational wave flux is finite and positive for asymptotically flat solutions.

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, $g_{\mu\nu}$. 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, $g_{[\mu\nu]}$, 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.