Covariant analysis of Newtonian multi-fluid models for neutron stars: II Stress-energy tensors and virial theorems

The 4-dimensionally covariant approach to multiconstituent Newtonian fluid dynamics presented in the preceding paper of this series is developed by construction of the relevant 4-dimensional stress-energy tensor whose conservation in the non-dissipative variational case is shown to be interpretable as a Noether identity of the Milne spacetime structure. The formalism is illustrated by the application to homogeneously expanding cosmological models, for which appropriately generalized local Bernoulli constants are constructed. Another application is to the Iordanski type generalization of the Joukowski formula for the Magnus force on a vortex. Finally, at a global level, a new (formally simpler but more generally applicable) version of the "virial theorem" is obtained for multiconstituent neutron or other fluid star models as a special case within an extensive category of formulae whereby the time evolution of variously weighted mass moment integrals is determined by corresponding space integrals of stress tensor components, with the implication that all such stress integrals must vanish for any stationary equilibrium configuration.