We study the linearized spin-2 field on conformally compactified Minkowski spacetime. Initial data are prescribed on past null infinity ${ℐ}^{-}$, and the system is evolved through the cylinder at spatial infinity to future null infinity ${ℐ}^{+}$. To avoid the development of logarithmic singularities and thereby preserve smooth peeling behavior, we derive explicit conditions on the freely specifiable ingoing gravitational radiation ${\psi }_0$ at ${ℐ}^{-}$ that ensure regular initial data. For compactly supported data, we obtain necessary and sufficient integral conditions guaranteeing regularity and compact support of the full system. In the simplest cases, we construct examples of exact initial data, while for the general case, we present a numerical procedure that computes the remaining ${\psi }_k$ to obtain a full initial dataset. 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 ${ℐ}^{-}$ to ${ℐ}^{+}$. These results provide a step toward a framework for fully global simulations of gravitational radiation and clarify the role of initial data on ${ℐ}^{-}$ in determining asymptotic structure.

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• General relativity
• Gravitation
• Gravitational waves