Field Equations and Conservation Laws in the Nonsymmetric Gravitational Theory

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.Comment: 16 pages, RevTeX. Additional equations supplie

Nonlocal Astroparticles in Einstein's Universe

Gravitational probes should maintain spatial flatness for Einsten-Infeld-Hoffmann dynamics of relativistic matter-energy. The continuous elementary source/particle in Einstein's gravitational theory is the r^{-4} radial energy density rather than the delta-operator density in empty-space gravitation. The space energy integral of such an infinite (astro)particle is finite and determines its nonlocal gravitational charge for the energy-to-energy attraction of other nonlocal (astro)particles. The non-empty flat space of the undivided material Universe is charged continuously by the world energy density of the global ensemble of overlapping radial particles. Nonlocal gravitational/inertial energy-charges incorporate Machian relativism quantitatively into Einstein's gravitation for self-contained SR-GR dynamics without references on Newton's mass-to-mass attraction.Comment: 9 pages, typos and arguments adde

Conformal Invariance in Einstein-Cartan-Weyl space

We consider conformally invariant form of the actions in Einstein, Weyl, Einstein-Cartan and Einstein-Cartan-Weyl space in general dimensions($>2$) and investigate the relations among them. In Weyl space, the observational consistency condition for the vector field determining non-metricity of the connection can be obtained from the equation of motion. In Einstein-Cartan space a similar role is played by the vector part of the torsion tensor. We consider the case where the trace part of the torsion is the Kalb-Ramond type of field. In this case, we express conformally invariant action in terms of two scalar fields of conformal weight -1, which can be cast into some interesting form. We discuss some applications of the result.Comment: 10 pages, version to appear MPL

The Dynamical Instability of Static, Spherically Symmetric Solutions in Nonsymmetric Gravitational Theories

We consider the dynamical stability of a class of static, spherically-symmetric solutions of the nonsymmetric gravitational theory. We numerically reproduce the Wyman solution and generate new solutions for the case where the theory has a nontrivial fundamental length scale \mu^{-1}. By considering spherically symmetric perturbations of these solutions we show that the Wyman solutions are generically unstable.Comment: 13 pages, uses amslatex, graphicx and subfigure package

Geodesic and Path Motion in the Nonsymmetric Gravitational Theory

We study the problem of test-particle motion in the Nonsymmetric Gravitational Theory (NGT) assuming the four-velocity of the particle is parallel-transported along the trajectory. The predicted motion is studied on a static, spherically symmetric background field, with particular attention paid to radial and circular motions. Interestingly, it is found that the proper time taken to travel between any two non-zero radial positions is finite. It is also found that circular orbits can be supported at lower radii than in General Relativity for certain forms of motion. We present three interactions which could be used as alternate methods for coupling a test-particle to the antisymmetric components of the NGT field. One of these takes the form of a Yukawa force in the weak-field limit of a static, spherically symmetric field, which could lead to interesting phenomenology.Comment: 17 pages, REVTeX 3.0 with amssymb.st

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

We investigate the possibility of constructing a locally supersymmetric extension of NGT (Nonsymmetric Gravitation Theory), based on the graded extension of the Poincare group. In the framework of the simple model that we propose, we end up with a no-go result, namely the impossibility of cancelling some linear contribution in the gravitino field. This drawback seems to seriously undermine the construction of a supergravity based on NGT.Comment: 17 pages, Latex,two references added, minor changes for clarity, v3: E-mail changed, v4 : Ref(9) correcte

On the nonsymmetric purely affine gravity

We review the vacuum purely affine gravity with the nonsymmetric connection and metric. We also examine dynamical effects of the second Ricci tensor and covariant second-rank tensors constructed from the torsion tensor in the gravitational Lagrangian.Comment: 15 pages; published versio

An assessment of Evans' unified field theory I

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe theta and a (metric compatible) Lorentz connection Gamma. These two potentials yield the field strengths torsion T and curvature R. Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe theta to be proportional to four extended electromagnetic potentials A; these are assumed to encompass the conventional Maxwellian potential in a suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans' ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.Comment: 39 pages of latex, modified because of referee report, mistakes and typos removed, partly reformulated, taken care of M.W.Evans' rebutta

The unexpected resurgence of Weyl geometry in late 20-th century physics

Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was withdrawn by its author from physical theorizing in the early 1920s. It had a comeback in the last third of the 20th century in different contexts: scalar tensor theories of gravity, foundations of gravity, foundations of quantum mechanics, elementary particle physics, and cosmology. It seems that Weyl geometry continues to offer an open research potential for the foundations of physics even after the turn to the new millennium.Comment: Completely rewritten conference paper 'Beyond Einstein', Mainz Sep 2008. Preprint ELHC (Epistemology of the LHC) 2017-02, 92 pages, 1 figur