Instabilities in the nonsymmetric theory of gravitation

TL;DR

This paper analyzes the linearized nonsymmetric theory of gravitation in expanding and Schwarzschild backgrounds, revealing inherent instabilities unless the theory is simplified, and argues these instabilities likely persist in the full nonlinear theory.

Contribution

It demonstrates that the nonsymmetric theory of gravitation develops fundamental instabilities unless restricted to a specific simple form, and discusses the implications for the full nonlinear theory.

Findings

Instabilities occur in the linearized nonsymmetric gravitation theory in certain backgrounds.

A particular simple form of the Lagrangian avoids these instabilities.

Adding constraints cannot eliminate the instabilities in the full theory.

Abstract

We consider the linearized nonsymmetric theory of gravitation (NGT) within the background of an expanding universe and near a Schwarzschild metric. We show that the theory always develops instabilities unless the linearized nonsymmetric lagrangian reduces to a particular simple form. This theory contains a gauge invariant kinetic term, a mass term for the antisymmetric metric-field and a coupling with the Ricci curvature scalar. This form cannot be obtained within NGT. Next we discuss NGT beyond linearized level and conjecture that the instabilities are not a relic of the linearization, but are a general feature of the full theory. Finally we show that one cannot add ad-hoc constraints to remove the instabilities as is possible with the instabilities found in NGT by Clayton.