Field Equations and Conservation Laws in the Nonsymmetric Gravitational Theory

TL;DR

This paper derives field equations and conservation laws in the nonsymmetric gravitational theory using a Lagrangian approach, establishing key identities and energy positivity in the radiation zone.

Contribution

It introduces a first-order formalism for the field equations and derives conservation laws, including generalized Bianchi identities, within the nonsymmetric gravitational framework.

Findings

Derived the field equations from a Lagrangian density.

Established conservation laws and tensor identities.

Proved energy positivity in the radiation zone.

Abstract

The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived. Among these are the generalized Bianchi identities and the law of energy-momentum conservation. The Lagrangian density is expanded to second-order, and treated as an ``Einstein plus fields'' theory. From this, it is deduced that the energy is positive in the radiation zone.