The Case Against Smooth Null Infinity IV: Linearised Gravity Around Schwarzschild -- An Overview

Abstract

This paper is the fourth in a series dedicated to the mathematically rigorous asymptotic analysis of gravitational radiation under astrophysically realistic setups. It provides an overview of the physical ideas involved in setting up the mathematical problem, the mathematical challenges that need to be overcome once the problem is posed, as well as the main new results we obtain in the companion paper [KM24]. From the physical perspective, this includes a discussion of how Post-Newtonian theory provides a prediction on the gravitational radiation emitted by $N$ infalling masses from the infinite past in the intermediate zone, i.e. up to some finite advanced time. From the mathematical perspective, we then take this prediction, together with the condition that there be no incoming radiation from $\mathcal{I}^-$, as a starting point to set up a scattering problem for the linearised Einstein vacuum equations around Schwarzschild and near spacelike infinity, and we outline how to solve this scattering problem and obtain the asymptotic properties of the scattering solution near $i^0$ and $\mathcal{I}^+$. The full mathematical details are presented in the companion paper [KM24].