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 ({\bf 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 the sum of the retarded time, the Euclidean distance and certain function $f$. 
Wen-ling Huang, Xiao Zhang