Relativistic Elasticity

TL;DR

This paper formulates a covariant relativistic elasticity theory applicable to any spacetime, extending classical elasticity into a relativistic framework with well-posed equations and local existence results.

Contribution

It develops a covariant Lagrangian formulation of relativistic elasticity applicable to arbitrary spacetimes, generalizing classical elasticity and establishing well-posedness.

Findings

The theory reduces to classical elasticity in the non-relativistic limit.

The field equations form a symmetric hyperbolic system, ensuring well-posedness.

Local-in-time existence and uniqueness theorems are established.

Abstract

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 non-relativistic limit . 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.