Fully Global Numerical Evolutions of the Linearised Spin-2 Equation

Abstract

We study the linearised spin-2 field on conformally compactified Minkowski spacetime. Initial data are prescribed on past null infinity $\mathscr{I}^-$, and the system is evolved through the cylinder at spatial infinity to future null infinity $\mathscr{I}^+$. To avoid logarithmic singularities and thereby preserve smooth peeling behaviour, we present conditions on the freely specifiable ingoing radiation $\psi_0$ on $\mathscr{I}^-$ for a full set of regular initial data on $\mathscr{I}^-$. Additionally, we show necessary and sufficient conditions for a full set of compactly supported initial data, and present a numerical procedure for constructing said initial data. We perform numerical evolutions using two gauges corresponding to compactification of either a neighbourhood of spatial infinity or the entire Minkowski spacetime, and demonstrate stable propagation of the system from $\mathscr{I}^-$ to $\mathscr{I}^+$. These results provide a step toward a framework for fully global simulations of gravitational radiation and clarify the role of initial data on $\mathscr{I}^-$ in determining asymptotic structure.