The PostNewtonian 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/c2. It is further shown that these postNewtonian 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 postNewtonian theory. Besides the equations of motion, an appropriate tensor form of the virial theorem is also derived.
 Publication:

The Astrophysical Journal
 Pub Date:
 November 1965
 DOI:
 10.1086/148432
 Bibcode:
 1965ApJ...142.1488C