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GR: Gravitation und Relativitätstheorie

GR 11: Grundlegende Probleme und allgemeiner Formalismus

GR 11.1: Fachvortrag

Mittwoch, 28. März 2001, 16:30–16:45, VII

Deduction of the metric of spacetime from linear (pre-metric) classical electrodynamics — •Friedrich W. Hehl — Inst.Theor.Physik, Universität zu Köln, 50923 Köln

Continuing our joint work with Obukhov and Rubilar, we start from an axiomatic approach to classical electrodynamics: (1) Electric charge conservation. (2) Lorentz force density. (3) Magnetic flux conservation. (4) Localization of energy-momentum. Thereby the Maxwell equations and the energy-momentum current of the electromagnetic field are provided on any 4-dimensional differential manifold that can be 1+3 decomposed. No metric and no connection are needed so far, i.e., gravity doesn’t interfere.

A linear ansatz (5a) between the electromagnetic excitation H=( D, H) and the field strength F=(E,B), together with the assumption (5b) of a so-called HF-symmetry, yields a duality operator that determines the conformally invariant part of the metric of spacetime. This deduction will be displayed and possible consequences discussed.

F.W.Hehl & Yu.N. Obukhov: Foundations of Classical Electrodynamics. Birkhäuser, Boston. To appear 2001/02. Yu.N. Obukhov, T. Fukui, G.F. Rubilar, Physical Review D62 (2000) 044050, and refs. given there.