Gioel Calabrese et al 2006 Class. Quantum Grav. 23 4829 doi:10.1088/0264-9381/23/15/004
Asymptotically null slices in numerical relativity: mathematical analysis and spherical wave equation tests
Gioel Calabrese, Carsten Gundlach and David Hilditch
Show affiliationsWe 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 Γ ~ Rn/2. While 1 < n ≤ 2 slices intersect 
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.
- PACS
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11.25.Mj Compactification and four-dimensional models
11.25.Hf Conformal field theory, algebraic structures
04.20.Gz Spacetime topology, causal structure, spinor structure
- MSC
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81T40 Two-dimensional field theories, conformal field theories, etc.
83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)
- Subjects
- Dates
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Issue 15 (7 August 2006)
Received 28 December 2005
Published 6 July 2006
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Asymptotically null slices in numerical relativity: mathematical analysis and spherical wave equation tests
Gioel Calabrese et al 2006 Class. Quantum Grav. 23 4829
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