On the relation between ADM and Bondi energy-momenta Ⅲ-perturbed radiative spatial infinity

In a vacuum spacetime equipped with the Bondi's radiating metric which is asymptotically flat at spatial infinity including gravitational radiation (Condition D), we establish the relation between the ADM total energy-momentum and the Bondi energy-momentum for perturbed radiative spatial infinity. The perturbation is given by defining the "real" time as the sum of the retarded time, the Euclidean distance and certain function f.