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On the derivation of the spacetime metric from linear electrodynamics

Andreas Gross·Guillermo F. Rubilar
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Abstract

In the framework of metric-free electrodynamics, we start with a {\em linear} spacetime relation between the excitation 2-form $H = ({\cal D}, {\cal H})$ and the field strength 2-form $F = ({E,B})$. This linear relation is constrained by the so-called closure relation. We solve this system algebraically and extend a previous analysis such as to include also singular solutions. Using the recently derived fourth order {\em Fresnel} equation describing the propagation of electromagnetic waves in a general {\em linear} medium, we find that for all solutions the fourth order surface reduces to a light cone. Therefrom we derive the corresponding metric up to a conformal factor.

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Andreas Gross, Guillermo F. Rubilar. 2001-07-13. On the derivation of the spacetime metric from linear electrodynamics. https://doi.org/10.1016/s0375-9601(01)00354-1

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