Test Matter in a Spacetime with Nonmetricity

Examples in which spacetime might become non-Riemannian appear above Planck energies in string theory or, in the very early universe, in the inflationary model. The simplest such geometry is metric-affine geometry, in which {\it nonmetricity} appears as a field strength, side by side with curvature and torsion. In matter, the shear and dilation currents couple to nonmetricity, and they are its sources. After reviewing the equations of motion and the Noether identities, we study two recent vacuum solutions of the metric-affine gauge theory of gravity. We then use the values of the nonmetricity in these solutions to study the motion of the appropriate test-matter. As a Regge-trajectory like hadronic excitation band, the test matter is endowed with shear degrees of freedom and described by a world spinor.Comment: 14 pages, file in late

Autoparallels From a New Action Principle

We present a simpler and more powerful version of the recently-discovered action principle for the motion of a spinless point particle in spacetimes with curvature and torsion. The surprising feature of the new principle is that an action involving only the metric can produce an equation of motion with a torsion force, thus changing geodesics to autoparallels. This additional torsion force arises from a noncommutativity of variations with parameter derivatives of the paths due to the closure failure of parallelograms in the presence of torsionComment: Paper in src. Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html Read paper directly with Netscape under http://www.physik.fu-berlin.de/~kleinert/kleiner_re243/preprint.htm

PP-waves with torsion and metric-affine gravity

A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a nonvanishing parallel spinor field; here the connection is assumed to be Levi-Civita. We generalise this definition to metric compatible spacetimes with torsion and describe basic properties of such spacetimes. We use our generalised pp-waves for constructing new explicit vacuum solutions of quadratic metric-affine gravity.Comment: 17 pages, LaTeX2

Is the Quantum Hall Effect influenced by the gravitational field?

Most of the experiments on the quantum Hall effect (QHE) were made at approximately the same height above sea level. A future international comparison will determine whether the gravitational field $\mathbf{g}(x)$ influences the QHE. In the realm of (1 + 2)-dimensional phenomenological macroscopic electrodynamics, the Ohm-Hall law is metric independent (`topological'). This suggests that it does not couple to $\mathbf{g}(x)$. We corroborate this result by a microscopic calculation of the Hall conductance in the presence of a post-Newtonian gravitational field.Comment: 4 page

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

Absolute spacetime: the twentieth century ether

All gauge theories need ``something fixed'' even as ``something changes.'' Underlying the implementation of these ideas all major physical theories make indispensable use of an elaborately designed spacetime model as the ``something fixed,'' i.e., absolute. This model must provide at least the following sequence of structures: point set, topological space, smooth manifold, geometric manifold, base for various bundles. The ``fine structure'' of spacetime inherent in this sequence is of course empirically unobservable directly, certainly when quantum mechanics is taken into account. This issue is at the basis of the difficulties in quantizing general relativity and has been approached in many different ways. Here we review an approach taking into account the non-Boolean properties of quantum logic when forming a spacetime model. Finally, we recall how the fundamental gauge of diffeomorphisms (the issue of general covariance vs coordinate conditions) raised deep conceptual problems for Einstein in his early development of general relativity. This is clearly illustrated in the notorious ``hole'' argument. This scenario, which does not seem to be widely known to practicing relativists, is nevertheless still interesting in terms of its impact for fundamental gauge issues.Comment: Contribution to Proceedings of Mexico Meeting on Gauge Theories of Gravity in honor of Friedrich Heh

A formal framework for a nonlocal generalization of Einstein's theory of gravitation

The analogy between electrodynamics and the translational gauge theory of gravity is employed in this paper to develop an ansatz for a nonlocal generalization of Einstein's theory of gravitation. Working in the linear approximation, we show that the resulting nonlocal theory is equivalent to general relativity with "dark matter". The nature of the predicted "dark matter", which is the manifestation of the nonlocal character of gravity in our model, is briefly discussed. It is demonstrated that this approach can provide a basis for the Tohline-Kuhn treatment of the astrophysical evidence for dark matter.Comment: 13 pages RevTex, no figures; v2: minor corrections, reference added, matches published versio

Projective Invariance and One-Loop Effective Action in Affine-Metric Gravity Interacting with Scalar Field

We investigate the influence of the projective invariance on the renormalization properties of the theory. One-loop counterterms are calculated in the most general case of interaction of gravity with scalar field.Comment: 10 pages, LATE