Nonsymmetric Gravity Theories: Inconsistencies and a Cure

TL;DR

This paper investigates nonsymmetric gravity theories, finds fundamental inconsistencies in most, and proposes a modified model with a massive antisymmetric tensor field that could lead to new gravitational phenomena.

Contribution

It demonstrates that standard second-derivative nonsymmetric gravity theories are inconsistent and introduces a modified model with mass terms to restore consistency and explore new physics.

Findings

Standard nonsymmetric gravity theories violate physical consistency.

Adding nonderivative terms gives mass to the antisymmetric tensor.

The modified model predicts novel gravitational effects.

Abstract

Motivated by the apparent dependence of string $\sigma$--models on the sum of spacetime metric and antisymmetric tensor fields, we reconsider gravity theories constructed from a nonsymmetric metric. We first show that all such "geometrical" theories homogeneous in second derivatives violate standard physical requirements: ghost-freedom, absence of algebraic inconsistencies or continuity of degree-of-freedom content. This no-go result applies in particular to the old unified theory of Einstein and its recent avatars. However, we find that the addition of nonderivative, ``cosmological'' terms formally restores consistency by giving a mass to the antisymmetric tensor field, thereby transmuting it into a fifth-force-like massive vector but with novel possible matter couplings. The resulting macroscopic models also exhibit ``van der Waals''-type gravitational effects, and may provide useful phenomenological foils to general relativity.