Center-of-mass theorem in post-Newtonian hydrodynamics

Abstract

In the post-Newtonian theory of a perfect fluid in adiabatic motion, the conservation laws of energy, momentum, and angular momentum can be obtained via Noether's theorem from the invariance properties of the Lagrangian under infinitesimal time and space translations and rotations, in complete analogy to the corresponding case of interacting particles; but, again in complete analogy, the center-of-mass theorem cannot be as directly related to the infinitesimal transformations of a group. Therefore the center-of-mass theorem had previously only been obtained by direct integration of the equations of motion. However, it has been shown recently in the case of interacting particles by Havas and Stachel that invariance of the Lagrangian under space and time translations is by itself sufficient to guarantee the existence of a center-of-mass theorem, and it is shown here that the techniques developed for that case also lead to the center-of-mass theorem for the perfect fluid. (AIP)