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Spacetime metric from linear electrodynamics II

Friedrich W. Hehl·Yuri N. Obukhov·Guillermo F. Rubilar
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Abstract

Following Kottler, É.Cartan, and van Dantzig, we formulate the Maxwell equations in a metric independent form in terms of the field strength $F=(E,B)$ and the excitation $H=({\cal D}, {\cal H})$. We assume a linear constitutive law between $H$ and $F$. First we split off a pseudo-scalar (axion) field from the constitutive tensor; its remaining 20 components can be used to define a duality operator $^#$ for 2-forms. If we enforce the constraint $^{##}=-1$, then we can derive of that the conformally invariant part of the {\em metric} of spacetime.

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Friedrich W. Hehl, Yuri N. Obukhov, Guillermo F. Rubilar. 1999-11-24. Spacetime metric from linear electrodynamics II. https://arxiv.org/abs/gr-qc/9911096

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