Relative continuum mechanics in general relativity

Summary An axiomatic approach to the study of relative continuum mechanics in curved space-time is proposed. The explicit assumptions are: a) existence of the energy-momentum tensor T^ij, satisfying the equations of motion T^ij _‖j=0, and b) existence of the congruence of stream-lines of the given continuum. The argument relies on a relativistic extension of the Lagrangian viewpoint, and involves the analysis of the relative dynamical behaviour of an arbitrary infinitestimal globule Δ of continuum in a given frame of reference Γ]. The plan is fulfilled in two steps:1) geometrical theory of the Lagrangian viewpoint, valid for any type of continua satisfying the stated requirements;2) physical applications, illustrating the general theory in the case of an energy-momentum tensor of the form T^ij=μ ₀ VⁱV^j—S^ij. Entrata in Redazione il 22 novembre 1977. Lavoro eseguito nell'ambito dell'attività del Gruppo Nazionale per la Fisica Matematica del C.N.R.