The post-Newtonian equations of hydrodynamics in general relativity

Abstract

The standard Eulerian equations of hydrodynamics are generalized to take into account, consistently with Einstein's field equations, all effects of order 1/c. It is further shown that these post-Newtonian equations allow integrals of motion which are entirely analogous to the Newtonian integrals that express the conservation of mass, linear momentum, angular momentum, and energy. The continued validity of these conservation laws enables a consistent definition of "mass", "momentum", and "energy" in the framework of the post-Newtonian theory. Besides the equations of motion, an appropriate tensor form of the virial theorem is also derived.