arXiv subjects

Friedrich W. Hehl

Publications and source records attributed to Friedrich W. Hehl.

At least 55 records · Page 3Linked to original sources

arXiv2009

Nonlocal Gravity Simulates Dark Matter

A nonlocal generalization of Einstein's theory of gravitation is constructed within the framework of the translational gauge theory of gravity. In the linear approximation, the nonlocal theory can be interpreted as linearized general relativity but in the presence of "dark matter" that can be simply expressed as an integral transform of matter. It is shown that this approach can accommodate the Tohline-Kuhn treatment of the astrophysical evidence for dark matter.

gr-qc↗

arXiv2008

On possible skewon effects on light propagation

We start from a local and linear spacetime relation between the electromagnetic excitation and the field strength. Then we study the generally covariant Fresnel surfaces for light rays and light waves. The metric and the connection of spacetime are left unspecified. Accordingly, our framework is ideally suited for a search of possible violations of the Lorentz symmetry in the photon sector of the extended standard model. We discuss how the skewon part of the constitutive tensor, if suitably parametrized, influences the Fresnel surfaces and disturbs the light cones of vacuum electrodynamics. Conditions are specified that yield the reduction of the original quartic Fresnel surface to the double light cone structure (birefringence) and to the single light cone. Qualitatively, the effects of the real skewon field can be compared to those in absorbing material media. In contrast, the imaginary skewon field can be interpreted in terms of non-absorbing media with natural optical activity and Faraday effects. The astrophysical data on gamma-ray bursts are used for deriving an upper limit for the magnitude of the skewon field.

physics.class-ph↗

arXiv2008

Maxwell's equations in Minkowski's world: their premetric generalization and the electromagnetic energy-momentum tensor

In December 1907, Minkowski expressed the Maxwell equations in the very beautiful and compact 4-dimensional form: lor f=-s, lor F^*=0. Here `lor', an abbreviation of Lorentz, represents the 4-dimensional differential operator. We study Minkowski's derivation and show how these equations generalize to their modern premetric form in the framework of tensor and exterior calculus (valid also in general relativity). After mentioning some applications of premetric electrodynamics, we turn to Minkowski's discovery of the energy-momentum tensor of the electromagnetic field. We discuss how he arrived at it and how its premetric formulation looks like.

gr-qc↗

arXiv2008

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.

physics.class-ph↗

arXiv2007

Elie Cartan's torsion in geometry and in field theory, an essay

We review the application of torsion in field theory. First we show how the notion of torsion emerges in differential geometry. In the context of a Cartan circuit, torsion is related to translations similar as curvature to rotations. Cartan's investigations started by analyzing Einsteins general relativity theory and by taking recourse to the theory of Cosserat continua. In these continua, the points of which carry independent translational and rotational degrees of freedom, there occur, besides ordinary (force) stresses, additionally spin moment stresses. In a 3-dimensional continuized crystal with dislocation lines, a linear connection can be introduced that takes the crystal lattice structure as a basis for parallelism. Such a continuum has similar properties as a Cosserat continuum, and the dislocation density is equal to the torsion of this connection. Subsequently, these ideas are applied to 4-dimensional spacetime. A translational gauge theory of gravity is displayed (in a Weitzenboeck or teleparallel spacetime) as well as the viable Einstein-Cartan theory (in a Riemann-Cartan spacetime). In both theories, the notion of torsion is contained in an essential way. Cartan's spiral staircase is described as a 3-dimensional Euclidean model for a space with torsion, and eventually some controversial points are discussed regarding the meaning of torsion.

gr-qc↗

arXiv2007

Comments on ``Spin Connection Resonance in Gravitational General Relativity''

We comment on a recent article of M.W.Evans, Acta Physica Polonica B38 (2007) 2211. We point out that the equations underlying Evans' theory are highly problematic. Moreover, we demonstrate that the so-called ``spin connection resonance'', predicted by Evans, cannot be derived from the equation he used. We provide an exact solution of Evans' corresponding equation and show that is has definitely no resonance solutions.

physics.class-ph↗

arXiv2007

Forces and momenta caused by electromagnetic waves in magnetoelectric media

We analyse the propagation of electromagnetic waves in magnetoelectric media. Recently, Feigel has predicted that such a medium may ``extract momentum from vacuum" in the sense that the total momentum of the virtual waves (vacuum fluctuations of the electromagnetic field) is nontrivial. Our aim is to check the feasibility of this effect. The crucial point in our study is an assumption of the finite size of the magnetoelectric sample, which allows us to reduce the calculation of the momenta and forces of the electromagnetic waves acting on the sample to the vacuum region outside of the medium. In this framework, we demonstrate that, in contrast to Feigel, the total force caused by the virtual is zero, with an appropriate count of the modes that should be taken into account in this effect. Furthermore, we find that the two irreducible parts of the magnetoelectric matrix behave differently in the possible Feigel effect. Going beyond the original scheme of the virtual electromagnetic waves, we propose an experimental scheme which is suitable for the measurement of the magnetoelectric susceptibilities of the medium with the help of real electromagnetic waves.

physics.class-ph↗

arXiv2007

Relativistic analysis of magnetoelectric crystals: extracting a new 4-dimensional P odd and T odd pseudoscalar from Cr_2 O_3 data

Earlier, the linear magnetoelectric effect of chromium sesquioxide Cr_2 O_3 has been determined experimentally as a function of temperature. One measures the electric field-induced magnetization on Cr_2 O_3 crystals or the magnetic field-induced polarization. From the magnetoelectric moduli of Cr_2 O_3 we extract a 4-dimensional relativistic invariant pseudoscalar \tildeα. It is temperature dependent and of the order of ~ 10^{-4} Y_0, with Y_0 as vacuum admittance. We show that the new pseudoscalar \tildeαis odd under parity transformation and odd under time inversion. Moreover, \tildeαis for Cr_2 O_3 what Tellegen's gyrator is for two port theory, the axion field for axion electrodynamics, and the PEMC (perfect electromagnetic conductor) for electrical engineering.

gr-qc↗

arXiv2007

Electrodynamics of moving magnetoelectric media: variational approach

Recently, Feigel has predicted a new effect in magnetoelectric media. The theoretical evaluation of this effect requires a careful analysis of a dynamics of the moving magnetoelectric medium and, in particular, the derivation of the energy-momentum of the electromagnetic field in such a medium. Then, one can proceed with the study of the wave propagation in this medium and derive the mechanical quantities such as the energy, the momentum, and their fluxes and the corresponding forces. In this paper, we develop a consistent general-relativistic variational approach to the moving dielectric and magnetic medium with and without magnetoelectric properties. The old experiments in which the light pressure was measured in fluids are reanalysed in our new framework.

gr-qc↗

arXiv2007

Relativistic nature of a magnetoelectric modulus of Cr_2O_3-crystals: a new 4-dimensional pseudoscalar and its measurement

Earlier, the magnetoelectric effect of chromium sesquioxide Cr_2O_3 has been determined experimentally as a function of temperature. One measures the electric field-induced magnetization on Cr_2O_3 crystals or the magnetic field-induced polarization. From the magnetoelectric moduli of Cr_2O_3 we extract a 4-dimensional relativistic invariant pseudoscalar $\widetildeα$. It is temperature dependent and of the order of 10^{-4}/Z_0, with Z_0 as vacuum impedance. We show that the new pseudoscalar is odd under parity transformation and odd under time inversion. Moreover, $\widetildeα$ is for Cr_2O_3 what Tellegen's gyrator is for two port theory, the axion field for axion electrodynamics, and the PEMC (perfect electromagnetic conductor) for electrical engineering.

cond-mat.other↗

arXiv2007

On the boundary-value problems and the validity of the Post constraint in modern electromagnetism

We recall that the theory of electromagnetism consists of three building blocks: (a) the inhomogeneous Maxwell equations for the electric and magnetic excitations $(D,H)$ (which reflects charge conservation), (b) the homogeneous Maxwell equations for the electric and magnetic field strengths $(E,B)$ (which reflects flux conservation), and (c) the constitutive relation between $(D,H)$ and $(E,B)$. In the recent paper \cite{Lakhtakia1}, Lakhtakia proposed to change the standard boundary conditions in electrodynamics in order to exclude certain constitutive parameters. We show that this is inadmissible both from the macroscopic and the microscopic points of view.

physics.class-ph↗

arXiv2007

Equivalence principle and electromagnetic field: no birefringence, no dilaton, and no axion

The coupling of the electromagnetic field to gravity is discussed. In the premetric axiomatic approach based on the experimentally well established conservation laws of electric charge and magnetic flux, the Maxwell equations are the same irrespective of the presence or absence of gravity. In this sense, one can say that the charge "substratum" and the flux "substratum" are not influenced by the gravitational field directly. However, the interrelation between these fundamental substrata, formalized as the {\it spacetime relation} H=H(F) between the 2-forms of the electromagnetic excitation H and the electromagnetic field strength F, is affected by gravity. Thus the validity of the equivalence principle for electromagnetism depends on the form of the spacetime relation. We discuss the nonlocal and local linear constitutive relations and demonstrate that the spacetime metric can be accompanied also by skewon, dilaton, and axion fields. All these premetric companions of the metric may eventually lead to a violation of the equivalence principle.

gr-qc↗

arXiv2007

An assessment of Evans' unified field theory II

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for Evans' theory and show that it yields two field equations. The second field equation is algebraic in the torsion and we can resolve it with respect to the torsion. It turns out that for all physical cases the torsion vanishes and the first field equation, together with Evans' unified field theory, collapses to an ordinary Einstein equation.

physics.class-ph↗

arXiv2006

A remark on an ansatz by M.W. Evans and the so-called Einstein-Cartan-Evans unified field theory

M.W.Evans tried to relate the electromagnetic field strength to the torsion of a Riemann-Cartan spacetime. We show that this ansatz is untenable for at least two reasons: (i) Geometry: Torsion is related to the (external) translation group and cannot be linked to an internal group, like the U(1) group of electrodynamics. (ii) Electrodynamics: The electromagnetic field strength as a 2-form carries 6 independent components, whereas Evans' electromagnetic construct F^\a is a vector-valued 2-form with 24 independent components. This doesn't match. One of these reasons is already enough to disprove the ansatz of Evans.

physics.class-ph↗

arXiv2006

Recent developments in premetric classical electrodynamics

Classical electrodynamics can be based on the conservation laws of electric charge and magnetic flux. Both laws are independent of the metric and the linear connection of spacetime. Within the framework of such a premetric electrodynamics -- provided a local and linear constitutive law of the vacuum is added -- the propagation of electromagnetic waves in the geometric-optics limit can be studied. The wave vectors of the wave fronts obey a quartic extended Fresnel equation. If one forbids birefringence in vacuum, the light cone emerges and Maxwell-Lorentz vacuum electrodynamics can be recovered. If minimal coupling of electrodynamics to gravity is assumed, then only the gravitational potential, i.e., the metric of spacetime, emerges in the constitutive law. We discuss recent results within this general framework.

physics.class-ph↗

arXiv2006

Linear connections with propagating spin-3 field in gravity

We show that Fronsdal's Lagrangian for a free massless spin-3 gauge field in Minkowski spacetime is contained in a general Yang--Mills-like Lagrangian of metric-affine gravity (MAG), the gauge theory of the general affine group in the presence of a metric. Due to the geometric character of MAG, this can best be seen by using Vasiliev's frame formalism for higher-spin gauge fields in which the spin-3 frame is identified with the tracefree nonmetricity one-form associated with the shear generators of GL(n,R). Furthermore, for specific gravitational gauge models in the framework of full nonlinear MAG, exact solutions are constructed, featuring propagating massless and massive spin-3 fields.

hep-th↗

arXiv2006

Rotating Black Holes in Metric-Affine Gravity

Within the framework of metric-affine gravity (MAG, metric and an independent linear connection constitute spacetime), we find, for a specific gravitational Lagrangian and by using {\it prolongation} techniques, a stationary axially symmetric exact solution of the vacuum field equations. This black hole solution embodies a Kerr-deSitter metric and the post-Riemannian structures of torsion and nonmetricity. The solution is characterized by mass, angular momentum, and shear charge, the latter of which is a measure for violating Lorentz invariance.

gr-qc↗

arXiv2005

Spacetime metric from local and linear electrodynamics: a new axiomatic scheme

We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically charged from neutral matter. Electric charge and magnetic flux are postulated to be conserved. As a consequence, the inhomogeneous and the homogeneous Maxwell equations emerge expressed in terms of the excitation H and the field strength F, respectively. H and F are assumed to fulfill a local and linear "spacetime relation" with 36 constitutive functions. The propagation of electromagnetic waves is considered under such circumstances in the geometric optics limit. We forbid birefringence in vacuum and find the light cone including its Lorentzian signature. Thus the conformally invariant part of the metric is recovered. If one sets a scale, one finds the pseudo-Riemannian metric of spacetime.

gr-qc↗