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We investigate the use of asymptotically null slices combined with stretchingor compactification of the radial coordinate for the numerical simulation ofasymptotically flat spacetimes. We consider a 1-parameter family of coordinatescharacterised by the asymptotic relation $r\sim R^{1-n}$ between the physicalradius $R$ and coordinate radius $r$, and the asymptotic relation $K\simR^{n/2-1}$ for the extrinsic curvature of the slices. These slices areasymptotically null in the sense that their Lorentz factor relative tostationary observers diverges as $\Gamma\sim R^{n/2}$. While $1<n\le 2$ slicesintersect $\scri$, $0< n\le 1$ slices end at $i^0$. We carry out numericaltests with the spherical wave equation on Minkowski and Schwarzschildspacetime. Simulations using our coordinates with $0<n\le 2$ achieve higheraccuracy at lower computational cost in following outgoing waves to very largeradius than using standard $n=0$ slices without compactification. Power-lawtails in Schwarzschild are also correctly represented.Comment: Numerical tests improved, conclusions extende

Asymptotically null slices in numerical relativity: mathematical analysis and spherical wave equation tests