Relativistic Electromagnetic Boundary Conditions

Ur, Hanoch

doi:10.2528/pier98101601

Cited by 4 publications

(3 citation statements)

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“…Our aim is to derive the metric-free and general relativistic covariant form of the jump conditions. This question was studied rather intensively, see [18], [19], [20], [21], [22], [23]. However, to our knowledge, a manifestly covariant and metric-free result was not yet presented in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…The number of independent boundary conditions in electromagnetism is discussed in literature, see [20], [21] and the references given therein. In the differential form notations, the boundary conditions are written as…”

Section: Independent Conditionsmentioning

confidence: 99%

“…Consequently, the four-dimensional surface current must be represented by a differential 3-form with a support on the surface. To deal with such singular currents, which are localized only on a surface ϕ(x i ) = 0, we define an even 1-form 21) referred to as Dirac's delta-form [27]. This is a type of a de Rham current, i.e., a singular differential form [26].…”

Section: Surface Currentmentioning

confidence: 99%

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Covariant jump conditions in electromagnetism

Itin

2012

Annals of Physics

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A generally covariant four-dimensional representation of Maxwell's electrodynamics in a generic material medium can be achieved straightforwardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic phenomena described by two tensor fields, which satisfy Maxwell's equations. A generic tensorial constitutive relation between these fields is an independent ingredient of the theory. By use of different constitutive relations (local and non-local, linear and non-linear, etc.), a wide area of applications can be covered. In the current paper, we present the jump conditions for the fields and for the energy-momentum tensor on an arbitrarily moving surface between two media. From the differential and integral Maxwell equations, we derive the covariant boundary conditions, which are independent of any metric and connection. These conditions include the covariantly defined surface current and are applicable to an arbitrarily moving smooth curved boundary surface. As an application of the presented jump formulas, we derive a Lorentzian type metric as a condition for existence the wave front in isotropic media. This result holds for the ordinary materials as well as for the metamaterials with the negative material constants.

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