The gravitational field in the wave zone. II: Consequences of asymptotic structure
[For part I, see the preceding review.] We consider an asymptotically flat and empty space-time generated by a bounded source of perfect fluid. The vanishing of the conformal Weyl tensor on \({\mathcal J}^+\) and of the Ricci tensor near \({\mathcal J}^+\) are used to simplify the expression obtained in the previous paper for the coefficient of \(r^{-1}\) of the metric tensor after an expansion in powers of \(c^{-1}\). The result is a very simple expression for the dominant term of \(g_{\alpha \beta 0}\) 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.
scientific article; zbMATH DE number 4011388