1,349 research outputs found
Covariant jump conditions in electromagnetism
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
Conserved currents for general teleparallel models
The obstruction for the existence of an energy momentum tensor for the
gravitational field is connected with differential-geometric features of the
Riemannian manifold. It has not to be valid for alternative geometrical
structures. In this article a general 3-parameter class of teleparallel models
is considered. The field equation turns out to have a form completely similar
to the Maxwell field equation d*\F^a=\T^a. By applying the Noether procedure,
the source 3-form \T^a is shown to be connected with the diffeomorphism
invariance of the Lagrangian. Thus the source of the coframe field is
interpreted as the total conserved energy-momentum current of the system. A
reduction of the conserved current to the Noether current and the Noether
charge for the coframe field is provided. An energy-momentum tensor for the
coframe field is defined in a diffeomorphism invariant and a translational
covariant way. The total energy-momentum current of a system is conserved. Thus
a redistribution of the energy-momentum current between material and coframe
(gravity) field is possible in principle, unlike as in GR. The energy-momentum
tensor is calculated for various teleparallel models: the pure Yang-Mills type
model, the anti-Yang-Mills type model and the generalized teleparallel
equivalent of GR. The latter case can serve as a very close alternative to the
GR description of gravity.Comment: 22 pages, 3 figure
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