Relativistic elasticity

Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially frame-indifferent case and, on Minkowski space, reduces to the latter in the limit c - (infinity). The field equations are cast into a first-order symmetric hyperbolic system. As a consequence, one obtains local-in-time existence and uniqueness theorems under various circumstances.