Relativistically Dynamic Elastic Dielectrics

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Abstract
A relativistically exact theory of elastic dielectrics is developed, plus incidentals useful in a wider context. The most general form of a relativistically objective elastic response function is found in terms of Bressan's deformation gradient and of arbitrary tensors on the body manifold depending on the Born strain tensor. A form for constitutive relations is postulated for dielectrics which involves objective response functions, physical laws are stated in terms of integrals of exterior forms on the world manifold, and the resultant differential equations of motion are derived. Facts about algebra and calculus of exterior forms are developed which will be useful in continuum physics whenever one introduces laws involving exterior forms on manifolds. The relation to historical theories of dielectrics is indicated.

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