A restatement of the normal form theorem for area metrics

Abstract

An area metric is a (0,4)-tensor with certain symmetries on a 4-manifold that represent a non-dissipative linear electromagnetic medium. A recent result by Schuller, Witte and Wohlfarth provides a pointwise normal form theorem for such area metrics. This result is similar to the Jordan normal form theorem for (1,1)-tensors, and the result shows that any area metric belongs to one of 23 metaclasses with explicit coordinate expressions for each metaclass. In this paper we restate and prove this result for skewon-free (2,2)-tensors and show that in general, each metaclasses has three different coordinate representations, and each of metaclasses I, II, ..., VI, VII need only one coordinate representation.

Updated proof of Proposition A.2 (Claim 5). Fixed typo in Theorem 6 (Metaclass XXIII)

References in corpus (5)

• Linear pre-metric electrodynamics and deduction of the light cone
• Causal structure and algebraic classification of area metric spacetimes in four dimensions
• The non-birefringent limit of all linear, skewonless media and its unique light-cone structure
• Propagation of light in area metric backgrounds
• Geometry of manifolds with area metric: multi-metric backgrounds

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• Geometry of Area Without Length
• Loop Special Relativity: Kaluza-Klein area metric as a line element for stringy events