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Friedrich W. Hehl

Publications and source records attributed to Friedrich W. Hehl.

At least 19 recordsLinked to original sources
arXiv2024

Violating Lorentz invariance minimally by the emergence of nonmetricity? A Perspective

Lorentz invariance belongs to the fundamental symmetries of nature. It is basic for the successful Standard Model of Particle Physics. Nevertheless, within the last decades, Lorentz invariance has been repeatedly questioned. In fact, there exist different research programs addressing this problem. We argue that a most adequate understanding of a possible violation of Lorentz invariance is achieved in the framework of the gauge-theoretic approach to gravity: a non-vanishing nonmetricity of a metric-affine geometry of spacetime heralds the violation of the Lorentz symmetry.

gr-qc↗
arXiv2023

Hyperfluid model revisited

A new variational theory of a hyperfluid is constructed which is free of the supplementary condition issue and provides a consistent model of the classical matter source in the metric-affine gravity theory.

gr-qc↗
arXiv2023

Nonmetricity and hypermomentum: on the possible violation of Lorentz invariance

We outline how the symmetry groups of spacetime are interpreted in a gauge-theoretic approach. Specifically, we focus on the hypermomentum concept and discuss the hyperfluid, that appropriately generalizes the perfect (Euler) fluid of general relativity to the case of continuous media with microstructure. We demonstrate that a possible violation of Lorentz invariance is most adequately understood by means of non-vanishing nonmetricity of a metric-affine geometry of spacetime.

gr-qc↗
arXiv2023

Motion of Test Particles in Spacetimes with Torsion and Nonmetricity

We derive the equations of motion of a test particle with intrinsic hypermomentum in spacetimes with both torsion $S$ and nonmetricity $Q$ (along with curvature $R$). Accordingly, $S$ and $Q$ can be measured by tracing out the trajectory followed by a hypermomentum-charged test particle in such a non-Riemannian background. The test particle is approximated by means of a Dirac $δ$-function. Thus we find a tangible way to observe and measure the effects of torsion and nonmetricity. Our results are consistent with earlier ones derived by Obukhov and Puetzfeld (2014) by means of a different method. We apply our insight and evaluate how far-reaching the so-called `geometrical trinity of gravity' really is.

gr-qc↗
arXiv2023

Four Lectures on Poincaré Gauge Field Theory

The Poincaré (inhomogeneous Lorentz) group underlies special relativity. In these lectures a consistent formalism is developed allowing an appropriate gauging of the Poincaré group. The physical laws are formulated in terms of points, orthonormal tetrad frames, and components of the matter fields with respect to these frames. The laws are postulated to be gauge invariant under local Poincaré transformations. This implies the existence of 4 translational gauge potentials ${e}^α$ (``gravitons") and 6 Lorentz gauge potentials $Γ^{αβ}$ (``rotons") and the coupling of the momentum current and the spin current of matter to these potentials, respectively. In this way one is led to a Riemann-Cartan spacetime carrying torsion and curvature, richer in structure than the spacetime of general relativity. The Riemann-Cartan spacetime is controlled by the two general gauge field equations (3.44) and (3.45), in which material momentum and spin act as sources. The general framework of the theory is summarized in a table in Section 3.6. -- Options for picking a gauge field lagrangian are discussed (teleparallelism, ECSK). We propose a lagrangian quadratic in torsion and curvature governing the propagation of gravitons and rotons. A suppression of the rotons leads back to general relativity.

gr-qc↗
arXiv2022

Gauge Theories of Gravitation

During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge theory of the Weyl-Cartan-Yang-Mills type. The present text offers commentaries on the articles from the most prominent proponents of the theory. In the early 1960s, the gauge idea was successfully applied to the Poincaré group of spacetime symmetries and to the related conserved energy-momentum and angular momentum currents. The resulting theory, the Poincaré gauge theory, encompasses Einstein's general relativity as well as the teleparallel theory of gravity as subcases. The spacetime structure is enriched by Cartan's torsion, and the new theory can accommodate fermionic matter and its spin in a perfectly natural way. This guided tour starts from special relativity and leads, in its first part, to general relativity and its gauge type extensions à la Weyl and Cartan. Subsequent stopping points are the theories of Yang-Mills and Utiyama and, as a particular vantage point, the theory of Sciama and Kibble. Later, the Poincaré gauge theory and its generalizations are explored and special topics, such as its Hamiltonian formulation and exact solutions, are studied. This guide to the literature on classical gauge theories of gravity is intended to be a stimulating introduction to the subject.

gr-qc↗
arXiv2020

Conservation of energy-momentum of matter as the basis for the gauge theory of gravitation

According to Yang \& Mills (1954), a {\it conserved} current and a related rigid (`global') symmetry lie at the foundations of gauge theory. When the rigid symmetry is extended to a {\it local} one, a so-called gauge symmetry, a new interaction emerges as gauge potential $A$; its field strength is $F\sim {\rm curl} A$. In gravity, the conservation of the energy-momentum current of matter and the rigid translation symmetry in the Minkowski space of special relativity lie at the foundations of a gravitational gauge theory. If the translation invariance is made local, a gravitational potential $\vartheta$ arises together with its field strength $T\sim {\rm curl}\,\vartheta$. Thereby the Minkowski space deforms into a Weitzenböck space with nonvanishing torsion $T$ but vanishing curvature. The corresponding theory is reviewed and its equivalence to general relativity pointed out. Since translations form a subgroup of the Poincaré group, the group of motion of special relativity, one ought to straightforwardly extend the gauging of the translations to the gauging of full Poincaré group thereby also including the conservation law of the {\it angular momentum} current. The emerging Poincaré gauge (theory of) gravity, starting from the viable Einstein-Cartan theory of 1961, will be shortly reviewed and its prospects for further developments assessed.

gr-qc↗
arXiv2020

Nonlocal Gravitomagnetism

We briefly review the current status of nonlocal gravity (NLG), which is a classical nonlocal generalization of Einstein's theory of gravitation based on a certain analogy with the nonlocal electrodynamics of media. Nonlocal gravity thus involves integro-differential field equations and a causal constitutive kernel that should ultimately be determined from observational data. We consider the stationary gravitational field of an isolated rotating astronomical source in the linear approximation of nonlocal gravity. In this weak-field and slow-motion approximation of NLG, we describe the gravitomagnetic field associated with the rotating source and compare our results with gravitoelectromagnetism (GEM) of the standard general relativity theory. Moreover, we briefly study the energy-momentum content of the GEM field in nonlocal gravity.

gr-qc↗
arXiv2019

Constitutive law of nonlocal gravity

We analyze the structure of a recent nonlocal generalization of Einstein's theory of gravitation by Mashhoon et al. By means of a covariant technique, we derive an expanded version of the nonlocality tensor which constitutes the theory. At the lowest orders of approximation, this leads to a simplification which sheds light on the fundamental structure of the theory and may prove useful in the search for exact solutions of nonlocal gravity.

gr-qc↗
arXiv2019

Physical dimensions/units and universal constants: their invariance in special and general relativity

The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing mechanics and electrodynamics, we are naturally led, besides the dimensions of length and time, to the fundamental units of action $\mathfrak h$, electric charge $q$, and magnetic flux $ϕ$. We have $q\times ϕ=\text{action}$ and $q/ϕ=1/\text{resistance}$. These results of \emph{classical physics} suggests to look into the corresponding quantum aspects of $q$ and $ϕ$ (and also of $\mathfrak h$): The electric charge occurs exclusively in elementary charges $e$, whereas the magnetic flux can have any value; in specific situations, however, in superconductors of type II at very low temperatures, $ϕ$ appears quantized in the form of fluxons (Abrikosov vortices). And $\mathfrak{h}$ leads, of course, to the Planck quantum $h$. Thus, we are directed to superconductivity and, because of the resistance, to the quantum Hall effect. In this way, the Josephson and the quantum Hall effects come into focus quite naturally. One goal is to determine the behavior of the fundamental constants in special and in general relativity, that is, if gravity is thought to be switched off versus the case in the gravitational field.

gr-qc↗
arXiv2018

Premetric teleparallel theory of gravity and its local and linear constitutive law

We continue to investigate the premetric teleparallel theory of gravity (TG) with the coframe (tetrad) as gravitational potential. We start from the field equations and a local and linear constitutive law. We create a Tonti diagram of TG in order to disclose the structure of TG. Subsequently we irreducibly decompose the 6th order constitutive tensor under the linear group. Moreover, we construct the most general constitutive tensors from the metric and the totally antisymmetric Levi-Civita symbol, and we demonstrate that they encompass nontrivial axion and skewon type pieces. Using these tools, we derive for TG in the geometric-optics approximation propagating massless spin 0, 1, and 2 waves, including the special case of Einstein's general relativity.

gr-qc↗
arXiv2017

Comparison of the DeWitt metric in general relativity with the fourth-rank constitutive tensors in electrodynamics and in elasticity theory

We perform a short comparison between the local and linear constitutive tensor $χ^{λνσκ}$ in four-dimensional electrodynamics (Sec.2), the elasticity tensor $c^{ijkl}$ in three-dimensional elasticity theory (Sec.3), and the DeWitt metric $G^{abcd}$ in general relativity, with ${a,b,\dots=1,2,3}$ (Sec.4). We find that the DeWitt metric has only six independent components.

gr-qc↗
arXiv2017

On Freud's superpotential in General Relativity and in Einstein-Cartan theory

The identification of a suitable gravitational energy in theories of gravity has a long history, and it is well known that a unique answer cannot be given. In the first part of this paper we present a streamlined version of the derivation of Freud's superpotential in general relativity. It is found if we once integrate the gravitational field equation by parts. This allows us to extend these results directly to the Einstein-Cartan theory. Interestingly, Freud's original expression, first stated in 1939, remains valid even when considering gravitational theories in Riemann-Cartan or, more generally, in metric-affine spacetimes.

gr-qc↗
arXiv2017

Premetric equivalent of general relativity: Teleparallelism

In general relativity (GR), the metric tensor of spacetime is essential since it represents the gravitational potential. In other gauge theories (such as electromagnetism), the so-called premetric approach succeeds in separating the purely topological field equation from the metric-dependent constitutive law. We show here that GR allows for a premetric formulation, too. For this purpose, we apply the teleparallel approach of gravity, which represents GR as a gauge theory based on the translation group. We formulate the metric-free topological field equation and a general linear constitutive law between the basic field variables. The requirement of local Lorentz invariance turns the model into a full equivalent of GR. Our approach opens a way for a natural extension of GR to diverse geometrical structures of spacetime.

gr-qc↗
arXiv2017

Gravity-induced four-fermion contact interaction implies gravitational intermediate W and Z type gauge bosons

Coupling fermions to gravity necessarily leads to a non-renormalizable, gravitational four-fermion contact interaction. In this essay, we argue that augmenting the Einstein-Cartan Lagrangian with suitable kinetic terms quadratic in the gravitational gauge field strengths (torsion and curvature) gives rise to new, massive propagating gravitational degrees of freedom. This is to be seen in close analogy to Fermi's effective four-fermion interaction and its emergent W and Z bosons.

gr-qc↗
arXiv2016

On Kottler's path: origin and evolution of the premetric program in gravity and in electrodynamics

In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this idea to Newton's gravitostatics and to Maxwell's electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical electrodynamics can be developed without a metric quite straightforwardly: the Maxwell equations, together with a local and linear response law for electromagnetic media, admit a consistent premetric formulation. Kottler's program succeeds here without provisos. In Kottler's approach to gravity, making the theory relativistic, two premetric quasi-Maxwellian field equations arise, but their field variables, if interpreted in terms of general relativity, do depend on the metric. However, one can hope to bring the Kottler idea to work by using the teleparallelism equivalent of general relativity, where the gravitational potential, the coframe, can be chosen in a premetric way.

gr-qc↗
arXiv2016

Generally Covariant Maxwell Theory for Media with a Local Response: Progress since 2000

In the recent decades, it became more and more popular for engineers, physicists, and mathematicians alike to put the Maxwell equations into a generally covariant form. This is particularly useful for understanding the fundamental structure of electrodynamics (conservation of electric charge and magnetic flux). Moreover, it is ideally suited for applying it to media with local (and mainly linear) response behavior. We try to collect the new knowledge that grew out of this development. We would like to ask the participants of EMTS 2016 to inform us of work that we may have overlooked in our review.

physics.class-ph↗