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

TL;DR

This paper investigates the relationship between ADM and Bondi energy-momenta in asymptotically flat vacuum spacetimes with gravitational radiation, focusing on perturbed radiative spatial infinity and defining a specific perturbation of the real time.

Contribution

It establishes a precise relation between ADM and Bondi energy-momenta in perturbed radiative spatial infinity with gravitational radiation.

Findings

Derived the relation between ADM and Bondi energy-momenta under perturbations.

Extended previous results to include gravitational radiation at spatial infinity.

Provided a new framework for analyzing perturbed radiative spacetimes.

Abstract

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 $f$.