Nonsymmetric Gravitational Theory Research Articles

Connections on a non-symmetric (generalized) Riemannian manifold and gravity

Connections with (skew-symmetric) torsion on a non-symmetric Riemannian manifold satisfying the Einstein metricity condition (non-symmetric gravitation theory (NGT) with torsion) are considered. It is shown that an almost Hermitian manifold is NGT with torsion if and only if it is a nearly Kähler manifold. In the case of an almost contact metric manifold the NGT with torsion spaces are characterized and a possibly new class of almost contact metric manifolds is extracted. Similar considerations lead to a definition of a particular class of almost para-Hermitian and almost paracontact metric manifolds. Conditions are given in terms of the corresponding Nijenhuis tensors and the exterior derivative of the skew-symmetric part of the non-symmetric Riemannian metric.

Implications of nonsymmetric metric theories for particle physics: New interpretation of the Pauli coupling

In this work, we provide a possible geometrical interpretation of the spin of elementary particles. In particular, it is investigated how the wave equations of matter are altered by the addition of an antisymmetric contribution to the metric tensor. In this scenario, the explicit form of the matter wave equations is investigated in a general curved spacetime, and then the equations are particularized to the flat case. Unlike traditional approaches of Nonsymmetric Gravitational Theories (NGT), in which the gravitational field is responsible for breaking the symmetry of the flat Minkowski metric, we find more natural to consider that, in general, the metric of the spacetime could be nonsymmetric even in the flat case. The physical consequences of this assumption are explored in detail. Interestingly enough, it is found that the metric tensor splits into a bosonic and a fermionic; the antisymmetric part of the metric is very sensitive to the spin and turns out to be undetectable for spinless scalar particles. However, fermions couple to it in a nontrivial way (only when there are interactions). In addition, the Pauli coupling is derived automatically as a consequence of the nonsymmetric nature of the metric.

Pulsar binary systems in a nonsymmetric theory of gravitation II. Dipole radiation

This paper deals with the emission of gravitational radiation in the context of a previously studied metric nonsymmetric theory of gravitation. The part coming from the symmetric part of the metric coincides with the mass quadrupole moment result of general relativity. The one associated to the antisymmetric part of the metric involves the dipole moment of the fermionic charge of the system. The results are applied to binary star systems and the decrease of the period of the elliptical motion is calculated.

Nonexistence of regular stationary solution in a metric nonsymmetric theory of gravitation

It is proven that the field equations of a previously studied metric nonsymmetric theory of gravitation do not admit any non-singular stationary solution which represents a field of non-vanishing total mass and non-vanishing total fermionic charge.

Problems and hopes in nonsymmetric gravity

We consider the linearized nonsymmetric theory of gravitation (NGT) within the background of an expanding universe and near a Schwarzschild mass. We show that the theory always develops instabilities unless the linearized nonsymmetric Lagrangian reduces to a particular simple form. This form contains a gauge-invariant kinetic term, a mass term for the anti-symmetric metric field and a coupling with the Ricci curvature scalar. This form cannot be obtained within NGT. Based on the linearized Lagrangian we know to be stable, we consider the generation and evolution of quantum fluctuations of the anti-symmetric gravitational field (B-field) from inflation up to the present day. We find that a B-field with a mass m ∝ 0.03(HI/1013 GeV)4 eV is an excellent dark matter candidate.

Analogue of the theorem of Birkhoff in a metric nonsymmetric theory of the gravitational-electromagnetic field

We prove that a spherically symmetric exterior solution of the field equations of a metric nonsymmetric theory of gravitation coupled with the electromagnetic field is necessarily static.

Vacuum properties of non-symmetric gravity in de Sitter space

We consider quantum effects of a massive antisymmetric tensor field on the dynamics ofde Sitter space–time. Our starting point is the most general, stable, linearizedLagrangian arising in non-symmetric gravitational theories, where part of theantisymmetric field mass is generated by the cosmological term. We construct arenormalization group (RG) improved effective action by integrating out one-loop vacuumfluctuations of the antisymmetric tensor field and show that, in the limit when the RGscale goes to zero, the Hubble parameter—and thus the effective cosmologicalconstant—relaxes rapidly to zero. We thus conclude that quantum loop effectsin de Sitter space can dramatically change the infrared sector of the on-shellgravity, making the expansion rate insensitive to the original (bare) cosmologicalconstant.

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.

Metric nonsymmetric theory of gravitation: the analogue of the theorem of Birkhoff

We prove that a spherically symmetric solution of the field equations of the metric nonsymmetric theory of gravitation developed previously is necessarily static.This is the analogue of the well known Birkhoff theorem in general relativity.

Instabilities in the nonsymmetric theory of gravitation

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 particularly 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 the 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.

Interior problem in a ponsymmetric theory of gravitation

The field equations of a previous metric nonsymmetric theory of gravitation are considered for the interior of a static spherically symmetric perfect fluid with a view to a study of stellar equilibrium. The equations are put into a form of four first-order differential equations which are ready for numerical integration.

The cosmology of the nonsymmetric theory of gravitation

We show that during cosmological inflation the nonsymmetric metric tensor theory of gravitation develops a spectrum which is potentially observable by cosmic microwave background observations, and may be the most sensitive probe of the scale of cosmic inflation.

Conservation laws in a metric nonsymmetric theory of gravitation

The conservation laws associated with a previously studied metric nonsymmetric theory of gravitation are established and their physical significance is discussed. Conservation laws are obtained for the generalized energy and momentum. Some applications of the results are made for a spherically symmetric fluid with a view to future study of stelar equilibrium.

Can a non-symmetric metric mimic NCQFT in $e^ + e^- \to \gamma \gamma$ ?

In the nonsymmetric gravitational theory (NGT) the space-time metric $g_{\mu\nu}$ departs from the flat-space Minkowski form $\eta_{\mu\nu}$ such that it is no longer symmetric, $i.e.$ $g_{\mu\nu} \ne g_{\nu\mu}$. 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 $e^+e^- \to \gamma\gamma$, both theories make the same striking prediction that the azimuthal cross section oscillates in $\phi$. However the predicted number of oscillations differs in the two theories: MNQFT predicts between one and four, whereas NCQFT has no such restriction.

Invariant length scale in relativistic kinematics: lessons from Dirichlet branes

Dirac–Born–Infeld theory is shown to possess a hidden invariance associated with its maximal electric field strength. The local Lorentz symmetry O(1,n) on a Dirichlet-n-brane is thereby enhanced to an O(1,n)×O(1,n) gauge group, encoding both an invariant velocity and acceleration (or length) scale. The presence of this enlarged gauge group predicts consequences for the kinematics of observers on Dirichlet branes, with admissible accelerations being bounded from above. An important lesson is that the introduction of a fundamental length scale into relativistic kinematics does not enforce a deformation of Lorentz boosts, as one might assume naively. The exhibited structures further show that Moffat's non-symmetric gravitational theory qualifies as a candidate for a consistent Born–Infeld type gravity with regulated solutions.

On the (im)possibility of a supersymmetric extension of NGT

We investigate the possibility of constructing a locally supersymmetric extension of nonsymmetric gravitation theory (NGT), based on the graded extension of the Poincaré group. In the framework of the simple model that we propose, we end up with a no-go result, namely the impossibility of cancelling out some linear contribution in the gravitino field. This drawback seems to seriously undermine the construction of a supergravity based on NGT.

Nonsymmetric gravitation theory in noncommutative geometry

We propose a reformulation of the nonsymmetric gravitation theory (NGT) in the context of noncommutative geometry. It is shown that all of the Moffat’s added terms in his new version of the NGT have a geometric origin.

Nonsymmetric unified field theory

A metric nonsymmetric unified theory of gravitation and electromagnetism is studied. By a suitable modification of the Einstein part of the Bonnor Lagrangian, it is shown that the antisymmetric part of the metric tensor can be made to describe a massless spin-1 field obeying Maxwell's equations in the flat space linear approximation and thus making its identification to the electromagnetic field strength tensor a possibly consistent procedure. The theory is shown to be free of unphysical ghost-negative energy radiative modes even when expanded about a curved Riemannian background. The Einstein-Maxwell theory is contained in the first approximation of the field equations about a curved general relativity background. The field equations contain only the symmetric part of the connection, making them as close as possible to those of general relativity. The equations of motion of charged particles are shown to contain the Coulomb force in the lowest nontrivial order of approximation.

Electromagnetism in a nonsymmetric theory of gravitation

The field equations of a proposed nonsymmetric theory of gravitation are derived when electro-magnetic fields are present, by adopting a nonminimal coupling which ensures the validity of the equivalence principle. The static and spherically symmetric solution of the field of a charged point particle is obtained.

Cauchy analysis of the linearized skew sector of the massive nonsymmetric gravitational theory

Cauchy analysis of the linearized field equations of the skew sector of the massive nonsymmetric gravitational theory shows that small perturbations give rise to bounded accelerations thereby ensuring good asymptotic behavior for the skew part of the fundamental tensor.