Linear pre-metric electrodynamics and deduction of the light cone

Abstract

We formulate a general framework for describing the electromagnetic properties of spacetime. These properties are encoded in the 'constitutive tensor of the vacuum', a quantity analogous to that used in the description of material media. We give a generally covariant derivation of the Fresnel equation describing the local properties of the propagation of electromagnetic waves for the case of the most general possible linear constitutive tensor. We also study the particular case in which a light cone structure is induced and the circumstances under which such a structure emerges. In particular, we will study the relationship between the dual operators defined by the constitutive tensor under certain conditions and the existence of a conformal metric. Closure and symmetry of the constitutive tensor will be found as conditions which ensure the existence of a conformal metric. We will also see how the metric components can be explicitly deduced from the constitutive tensor if these two conditions are met. Finally, we will apply the same method to explore the consequences of relaxing the condition of symmetry and how this affects the emergence of the light cone. * Email: grubilar at udec dot cl.

Gravitational dynamics for all tensorial spacetimes carrying predictive, interpretable, and quantizable matter

“…For our simple example of a Klein-Gordon field on a metric geometry, the determinant in (2) is of weight zero, and for the choice ρ = 1 we obtain P i 1 i 2 = G i 1 i 2 , and one indeed recovers the familiar massless dispersion relation G a 1 a 2 k a 1 k a 2 = 0. An instructive non-metric example is provided by abelian gauge theory coupled to an inverse area metric tensor geometry [11,12], which is based on a fourth rank contravariant tensor field G featuring the algebraic symmetries G abcd = G cdab = −G bacd ; calculation of the principal polynomial (after removing gauge-invariance, observing resulting constraints on initial conditions and re-covariantizing the expression) one obtains [10,13,14] in dim M = d dimensions the totally symmetric tensor field…”

Possible skewon effects on light propagation

“…The skewon contributions in (24) and (25) are responsible for the electric and magnetic Faraday effects, respectively, whereas skewon terms in (26) and (27) describe optical activity.…”

“…Here we briefly summarize the results of previous work [6,22,26,27]. In the Hadamard approach, one studies the propagation of a discontinuity in the first derivative of the electromagnetic field.…”

Torsion nonminimally coupled to the electromagnetic field and birefringence

“…We have shown in the past (see [13,14]) how one can determine light propagation in an arbitrary spacetime by means of a generalized Fresnel equation provided a linear spacetime relation H = κ(F ), or in components H αβ = 1 2 κ αβ γδ F γδ , is specified. Recently, we applied this method also to nonlinear electrodynamics, see [15].…”