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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 beyondAlberto Favaro1 and •Friedrich W. Hehl21Imperial 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, KR3. 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

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