On the derivation of the spacetime metric from linear electrodynamics

Details On the derivation of the spacetime metric from linear electrodynamics On the derivation of the spacetime metric from linear electrodynamics

2001-03-06

arxiv.org/abs/gr-qc/0103016v2

Phys.Lett. A285 (2001) 267-272

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 Pages, LaTeX, some typos corrected, one reference added. Version published in Physics Letters A

Scientific paper

10.1016/S0375-9601(01)00354-1

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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