A spacetime description of relativistic media

Abstract

A discussion is given of relativistic balance laws that may be used to construct models of material media with spin and electromagnetic properties, interacting with general background electromagnetic fields and gravitation described by non-Riemannian geometries. The general framework offers an approximation scheme for modelling relativistic media by supplementing the balance laws with conditions that convert them into an involutive differential system.

†Special symposium in honour of 2003 SES Eringen medalist, Gerard Maugin.

Acknowledgements

The author is most grateful to Tekin Dereli and Miguel Sánchez for useful conversations and BAe Systems for partial support. Particular thanks are also due to Adam Noble and David Burton for a careful reading of the manuscript.

Notes

†Special symposium in honour of 2003 SES Eringen medalist, Gerard Maugin.

†In theories with gravitational scalar fields it is possible to extend the local gauge symmetries to include Weyl scale covariance and an associated connection 1-form.

†To lowest non-trivial order the calculations below are insensitive to the precise fall off with λ.

‡In terms of an orthonormal basis the volume form ☆ 1 is chosen as e ⁰ ∧ e ¹ ∧e ² ∧ e ³.

† Strings arise as a special case of shear-free rods.

† In these expression F′ ≡ (∥/∂σ) F and .