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

Calabrese, Gioel, Gundlach, Carsten and Hilditch, David (2006) Asymptotically null slices in numerical relativity: mathematical analysis and spherical wave equation. Classical and Quantum Gravity, 23, 4829-4845. (doi:10.1088/0264-9381/23/15/004).

Record type: Article

Abstract

We investigate the use of asymptotically null slices combined with stretching or compactification of the radial coordinate for the numerical simulation of asymptotically flat spacetimes. We consider a 1-parameter family of coordinates characterized by the asymptotic relation r ~ R1-n between the physical radius R and the coordinate radius r, and the asymptotic relation K ~ Rn/2-1 for the extrinsic curvature of the slices. These slices are asymptotically null in the sense that their Lorentz factor relative to stationary observers diverges as ? ~ Rn/2. While 1 < n ? 2 slices intersect {\mathscr I^+}, 0< n\le 1 slices end at i0. We carry out numerical tests with the spherical wave equation on Minkowski and Schwarzschild spacetimes. Simulations using our coordinates with 0 < n ? 2 achieve higher accuracy at a lower computational cost in following outgoing waves to a very large radius than using standard n = 0 slices without compactification. Power-law tails in Schwarzschild are also correctly represented.

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