Conservation Laws in General Relativity and in the Post-Newtonian Approximations

It is shown how the exact conservation laws of general relativity, expressed in terms of the symmetric energy-momentum complex of Landau and Lifshitz, can be used to determine the various conserved quantities in the different post-Newtonian approximations. Particular attention is given to the conserved energy which emerges as the integral over the whole of space of the difference between the (0,0)-com- ponent of the Landau-Lifshitz complex and the energy of the conserved mass present. The method is illustrated in the framework of the first post-Newtonian equations of hydrodynamics