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We solve, numerically, the massless spin-2 equations, written in terms of agauge based on the properties of conformal geodesics, in a neighbourhood ofspatial infinity using spectral methods in both space and time. This strategyallows us to compute the solutions to these equations up to the critical setswhere null infinity intersects with spatial infinity. Moreover, we use theconvergence rates of the numerical solutions to read-off their regularityproperties.

Spectral methods for the spin-2 equation near the cylinder at spatial infinity