On the energy-momentum tensor of matter in the special theory of relativity (Q1174096)

The paper deals with the problem of uniqueness of the energy-momentum tensor of a continuous medium in special relativity. The author uses Sedov's thermodynamic variational equation, which enables one to construct models of nonconservative thermodynamic systems taking into account irreversible processes. As a result, the author gets two proper tensors, one symmetrical (T) and one nonsymmetrical (P), both tensors satisfying the momentum equation \[ \nabla_ jT^{ij}=\nabla_ jP^{ij}=Q^ i, \] where \(Q^ i\) are the components of the four- dimensional external body force vector. However, as the author shows, the initial and boundary conditions for the momentum equation are stated only for the uniquely calculated nonsymmetrical tensor \(P\). And this confirms the known fact, that the form of the conditions on surfaces of strong discontinuities (contained in the initial and boundary conditions) cannot be derived from the Euler equations.