Hamburg 2016 – wissenschaftliches Programm

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GR: Fachverband Gravitation und Relativitätstheorie

GR 11: Classical General Relativity II

GR 11.1: Hauptvortrag

Donnerstag, 3. März 2016, 13:45–14:25, VMP6 HS A

Fresnel-Kummer wave surfaces in transparent (meta)materials, the Kummer tensor in general relativity, and beyond — Alberto Favaro¹ and •Friedrich W. Hehl² — ¹Imperial College London — ²Univ. of Cologne and Univ. of Missouri, Columbia

The premetric Maxwell equations are expressed in terms of the excitations (D,H) and field strengths (E,B). A material with local and linear constitutive law carries, besides permittivities and permeabilities, magnetoelectric terms. In a spacetime description, this yields a 4th rank constitutive tensor χ with 36 = 20+15+1 independent components. We restrict ourselves to the reversible case with 21 components. The light propagation in such a material is described by quartic Fresnel surfaces, which are determined by a 4th rank tensor G cubic in χ, that is, G∼χ³. We show that these Fresnel surfaces are Kummer surfaces (from algebraic geometry) and study some of their singularities. — In general relativity, we can define analogously a 4th rank Kummer tensor K that is cubic in the 20 compoment Riemann tensor R, that is, K∼ R³. The Kummer tensor is related to the Petrov classification of the gravitational field. We generalize these results to the Poincaré gauge theory of gravity with a 36 components curvature tensor.

See Baekler, Favaro, Itin, fwh, Ann. Phys. (NY) 349, 297 (2014); Favaro, fwh, arXiv:1510.05566v1