Spacetime metric from linear electrodynamics II

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 $H=(\mathcal{D},\mathcal{H})$. 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.

11 pages, Latex-script, Based on a talk given at the `International European Conference on Gravitation: Journées Relativistes 99.' Weimar, Germany, 12-17 Sep 1999. Annalen der Physik, to appear (2000)