Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme

Hehl, Friedrich W.; Obukhov, Yuri N.

doi:10.1007/3-540-34523-x_7

Cited by 42 publications

(82 citation statements)

References 53 publications

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“…In order to understand the coupling of electromagnetism to gravity, it is most convenient and reasonable to start from the premetric formulation of the electrodynamical theory. Following the early work of Kottler, Cartan, and van Dantzig, one can indeed develop an axiomatic approach to the electromagnetic field [3,4,5] without assuming any specific geometric structure beyond the differentiable structure of the spacetime manifold, see also [6,7]. At the heart of this approach, there are the well established experimental facts (that can be formulated as fundamental axioms) of electric charge and magnetic flux conservation.…”

Section: Premetric Formulation Of Electrodynamicsmentioning

confidence: 99%

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

Hehl

Obukhov

2008

Gen Relativ Gravit

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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 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.

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Section: Premetric Formulation Of Electrodynamicsmentioning

confidence: 99%

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

Hehl

Obukhov

2008

Gen Relativ Gravit

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“…[1,2,9] spacetime tensors satisfying a so-called closure relation have been studied, namely those with…”

Section: Closure Relationmentioning

confidence: 99%

On the derivation of the spacetime metric from linear electrodynamics

Groß¹,

Rubilar²

2001

Physics Letters A

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In the framework of metric-free electrodynamics, we start with a linear spacetime relation between the excitation 2-form H = (D, H) and the field strength 2-form F = (E, B). This linear relation is constrained by the so-called closure relation. We solve this system algebraically and extend a previous analysis such as to include also singular solutions. Using the recently derived fourth order Fresnel equation describing the propagation of electromagnetic waves in a general linear medium, we find that for all solutions the fourth order surface reduces to a light cone. Therefrom we derive the corresponding metric up to a conformal factor.

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“…Based on previous works (see [3] and references therein), Hehl and Obukhov [3][4][5][6][7] clarified that this formalism is well established on four main postulates or axioms. These are charge conservation, magnetic flux conservation, Lorentz force and the constitutive relations between the fields (E, B) and excitations (D, H).…”

Section: Introductionmentioning

confidence: 99%

“…The first three have a good experimental basis while the last postulate, which usually considers linear, local, homogeneous and isotropic relations, is not so well supported by experiment. These relations in vacuum can be understood as expressing constitutive relations for the spacetime itself [6,7]. There is, one could say, a greater freedom in changing this postulate than the other three.…”

Section: Introductionmentioning

confidence: 99%

“…Such alternative or extended electromagnetic theories can and should be tested experimentally in the context of the coupling between electromagnetic fields and gravity. Indeed, already at the foundational level there is an intimate link between spacetime geometry, in particular, the conformal structure, and electrodynamics via the constitutive relations [6,7]. In this work, we start by considering linear, local, homogeneous and isotropic constitutive relations and study the effect of spacetime geometry on electromagnetic fields for specific physical situations.…”

Section: Introductionmentioning

confidence: 99%

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Electrodynamics and spacetime geometry: Astrophysical applications

Cabral

2017

Eur. Phys. J. Plus

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After a brief review of the foundations of (pre-metric) electromagnetism, we explore some physical consequences of electrodynamics in curved spacetime. In general, new electromagnetic couplings and related phenomena are induced by the spacetime curvature. The applications of astrophysical interest considered here correspond essentially to the following geometries: the Schwarzschild spacetime and the spacetime around a rotating spherical mass in the weak field and slow rotation regime. In the latter, we use the Parameterised Post-Newtonian (PPN) formalism. We also explore the hypothesis that the electric and magnetic properties of vacuum reflect the spacetime isometries. Therefore, the permittivity and permeability tensors should not be considered homogeneous and isotropic a priori. For spherical geometries we consider the effect of relaxing the homogeneity assumption in the constitutive relations between the fields and excitations. This affects the generalized Gauss and Maxwell-Ampère laws where the electric permittivity and magnetic permeability in vacuum depend on the radial coordinate in accordance with the local isometries of space. For the axially symmetric geometries we relax both the assumptions of homogeneity and isotropy. We explore simple solutions and discuss the physical implications related to different phenomena such as: the decay of electromagnetic fields in the presence of gravity, magnetic terms in Gauss law due to the gravitomagnetism of the spacetime around rotating objects, a frame-dragging effect on electric fields and the possibility of a spatial (radial) variability of the velocity of light in vacuum around spherical astrophysical objects for strong gravitational fields.

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Spacetime Metric from Local and Linear Electrodynamics: A New Axiomatic Scheme

Cited by 42 publications

References 53 publications

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

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

On the derivation of the spacetime metric from linear electrodynamics

Electrodynamics and spacetime geometry: Astrophysical applications

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