In this work, starting from the predictions of the Post-Newtonian theory for a system of N infalling masses from the infinite past \(i^-\) , we formulate and solve a scattering problem for the system of linearised gravity around Schwarzschild in a double null gauge, as introduced in Dafermos (Acta Math 222:1–214, 2019). The scattering data are posed on a null hypersurface \(\underline{\mathcal {C}}\) emanating from a section of past null infinity \(\mathcal {I}^{-}\) , and on the part of \(\mathcal {I}^{-}\) that lies to the future for this section. Along \(\underline{\mathcal {C}}\) , we implement the Post-Newtonian theory-inspired hypothesis that the gauge-invariant components of the Weyl tensor and (a.k.a. \(\Psi _0\) and \(\Psi _4\) ) decay like \(r^{-3}\) , \(r^{-4}\) , respectively, and we exclude incoming radiation from \(\mathcal {I}^{-}\) by demanding the News function to vanish along \(\mathcal {I}^{-}\) . We also show that compactly supported gravitational perturbations along \(\mathcal {I}^{-}\) induce very similar data, with , decaying like \(r^{-3}\) , \(r^{-5}\) . After constructing the unique solution to this scattering problem, we then provide a complete analysis of the asymptotic behaviour of projections onto fixed spherical harmonic number \(\ell \) near \(\mathcal {I}^{-}\) , spacelike infinity \(i^0\) and future null infinity \(\mathcal {I}^{+}\) , crucially exploiting a set of approximate conservation laws enjoyed by and . Having obtained a clear understanding of the asymptotics of linearised gravity around Schwarzschild, we also give constructive corrections to popular historical notions of asymptotic flatness such as Bondi coordinates or asymptotic simplicity. In particular, confirming earlier heuristics authorized by Damour and Christodoulou, we find that the peeling property is violated both near \(\mathcal {I}^{-}\) and near \(\mathcal {I}^{+}\) , with for example near \(\mathcal {I}^{+}\) only decaying like \(r^{-4}\) instead of \(r^{-5}\) . We also find that the resulting solution decays slower towards \(i^0\) than often assumed, with both decaying like \(r^{-3}\) towards \(i^0\) . The issue of summing up the estimates obtained for fixed angular modes in \(\ell \) in order to obtain asymptotics for the full solution is dealt with in forthcoming work.
