The gravitational field in the wave zone II. Consequences of asymptotic structure

We consider an asymptotically flat and empty space-time generated by a bounded source of perfect fluid. The vanishing of the conformal Weyl tensor onI⁺ and of the Ricci tensor nearI⁺ are used to simplify the expression obtained in the previous paper for the coefficient ofr^– of the metric tensor after an expansion in powers ofc^–1. The result is a very simple expression for the dominant term ofg_,0 in the radiation zone in terms of the quadrupole moment of the source. Using this expression and an invariant definition of the total energy, we calculate in the framework of full general relativity the radiated energy per unit time and prove that the first term is identical with the quadrupole radiation as given by the linearized version of general relativity.