On the derivation of the spacetime metric from linear electrodynamics

In the framework of metric-free electrodynamics, we start with a linear spacetime relation between the excitation 2-form H = (D, 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 Fresnel equation describing the propagation of electromagnetic waves in a general linear medium, we find that for all solutions the fourth-order surface reduces to a light cone. Therefore we derive the corresponding metric up to a conformal factor. (C) 2001 Elsevier Science B.V. All rights reserved.