On the derivation of the spacetime metric from linear electrodynamics

In the framework of metric-free electrodynamics, we start with a linear spa cetime relation between the excitation 2-form H = (D, H) and the field stre ngth 2-form F = (E, B). This linear relation is constrained by the so-calle d closure relation. We solve this system algebraically and extend a previou s analysis such as to include also singular solutions. Using the recently d erived fourth-order Fresnel equation describing the propagation of electrom agnetic waves in a general linear medium, we find that for all solutions th e fourth-order surface reduces to a light cone. Therefore we derive the cor responding metric up to a conformal factor. (C) 2001 Elsevier Science B.V. All rights reserved.