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.

Boyer–Lindquist Space-Times and Beyond: Metamaterial Analogues for Arbitrary Space-Times

“…For scalar permittivity and permeability, this gives the compatibility condition ϵ = µ of the above quote from Landau and Lifshitz [5]. The tensorial generalization to ϵ ij = µ ij was then rederived several times in the literature with different inspirations [16,45,46]. Even the most general cases can always (at least locally) be reduced to this case by appropriate frame changes [1].…”

Kinetic gases in static spherically symmetric modified dispersion relations

“…This quantum interaction would become manifest in a dispersion relation which is close to that given by GR at low energies, but exhibits larger deviations at higher energies. Commonly studied example of MDRs include models derived from doubly or deformed special relativity (DSR) [9][10][11], more generally deformed relativistic kinematics [12][13][14][15], non-commutative spacetime geometries [16][17][18][19], string theory [20,21], loop quantum gravity [22][23][24][25], the Standard-Model Extension (SME) [26], as well as the propagation of fields through media [27][28][29][30][31][32][33][34].…”