SPIN FROM THE NONSYMMETRIC METRIC TENSOR

A solution to the gravitational field equations based on a nonsymmetric metric tensor is examined. Unlike Einstein's interpretation of electromagnetism, or Moffat's generalized gravity, it is shown that the nonsymmetric part of the metric tensor is the potential of the spin field, and its intimate connection to string theory is established. This formulation solves the longstanding problem of electromagnetism and torsion, naturally showing how electromagnetism, through its intrinsic spin, can create torsion.

Can a Nonsymmetric Metric mimic NCQFT in e+e- → γγ?

In the nonsymmetric gravitational theory (NGT) the space-time metric gμν departs from the flat-space Minkowski form ημν such that it is no longer symmetric, i.e.gμν ≠ gνμ. We find that in the most conservative such scenario coupled to quantum field theory, which we call Minimally Nonsymmetric Quantum Field Theory (MNQFT), there are experimentally measurable consequences similar to those from noncommutative quantum field theory (NCQFT). This can be expected from the Seiberg-Witten map which has recently been interpreted as equating gauge theories on noncommutative spacetimes with those in a field dependent gravitational background. In particular, in scattering processes such as the pair annihilation e+e- → γγ, both theories make the same striking prediction that the azimuthal cross section oscillates in ϕ. However the predicted number of oscillations differs in the two theories: MNQFT predicts between one and four, whereas NCQFT has no such restriction.

Post-Newtonian expansion of an algebraically extended theory of gravity

The post-Newtonian expansion is analyzed for an algebraically extended theory of gravity equivalent to a theory with a real, nonsymmetric metric, previously referred to as Algebraically Extended Hilbert Gravity (AHG). The hermiticity of the algebra-valued covariant and contravariant metrics is found to constrain the form of the expansion of the antisymmetric part of the real metric to one of two possibilities. Both of these display a qualitatively new technical feature: the lowest order equations are nonlinear, depriving the post-Newtonian expansion of its greatest asset. In one case, they lead to a solution with a negative Newtonian mass parameter. In the other case, they lead to a contact-type solution in which some metric components depend directly upon the stress–energy tensor rather than the integral of this distribution. The unphysical nature of these solutions rules out AHG as a physically viable alternative theory of gravitation.