Massive NGT and Spherically Symmetric Systems

TL;DR

This paper reviews the massive Nonsymmetric Gravitational Theory (NGT), analyzing spherically symmetric perturbations, and shows that Birkhoff's theorem does not hold in NGT, implying the need for time-dependent exteriors in such systems.

Contribution

It provides a detailed analysis of spherically symmetric perturbations in NGT, demonstrating the breakdown of Birkhoff's theorem and discussing implications for the theory's global behavior.

Findings

Spherically symmetric systems in NGT are not necessarily static.

Birkhoff's theorem does not apply in NGT.

No energy flux in the monopole mode considered.

Abstract

The arguments leading to the introduction of the massive Nonsymmetric Gravitational action are reviewed \cite{Moffat:1994,Moffat:1995b}, leading to an action that gives asymptotically well-behaved perturbations on GR backgrounds. Through the analysis of spherically symmetric perturbations about GR (Schwarzschild) and NGT (Wyman-type) static backgrounds, it is shown that spherically symmetric systems are not guaranteed to be static, and hence Birkhoff's theorem is not valid in NGT. This implies that in general one must consider time dependent exteriors when looking at spherically symmetric systems in NGT. For the surviving monopole mode considered here there is no energy flux as it is short ranged by construction. Further work on the spherically symmetric case will be motivated through a discussion of the possibility that there remain additional modes that do not show up in weak field situations, but nonetheless exist in the full theory and may again result in bad global asymptotics. A presentation of the action and field equations in a general frame is given in the course of the paper, providing an alternative approach to dealing with the algebraic complications inherent in NGT, as well as offering a more general framework for discussing the physics of the antisymmetric sector.