Pseudomomentum in relativistic continuum mechanics

Abstract

In classical continuum mechanics the balance or unbalance equation of pseudomomentum reflects the material invariance of the system under study. It relates the time derivative of pseudo-momentum and the flux of the Eshelby stress. It is legitimate to inquire whether this structure is conserved in a relativistic four-dimensional background. We examine here the relativistic definition of pseudo/matertal momentum using simultaneously variational and direct approaches (the latter using the canonical projection of space-time onto the material manifold). It appears that the truly material entities, just as those in a proper frame, should be the basic ones, being independent of the relativity framework used.