Elasticity Theory in General Relativity

Abstract

An elasticity theory in general relativity is formulated and includes a measure of the strain which is identical to the classical concept. The theory is developed essentially by generalizing the classical elasticity theory. The physical interpretation of the work is simplified by retaining the three-dimensional form of the classical quantities. As a further aid to understanding the theory, some of the thermodynamics and the weak-field limit are studied. As part of the latter investigation the classical theory is reformulated so that there is no explicit dependence on the displacement u. The resulting equations near a strong similarity to the general-relativistic field equations when they are cast in a manner called the (3+1) form.