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

Asymptotically null slices in numerical relativity: mathematical analysis and spherical wave equation
Asymptotically null slices in numerical relativity: mathematical analysis and spherical wave equation
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.
0264-9381
4829-4845
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Hilditch, David
108ec927-5127-4228-86d5-493291f22021
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Hilditch, David
108ec927-5127-4228-86d5-493291f22021

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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More information

Published date: July 2006

Identifiers

Local EPrints ID: 54070
URI: https://eprints.soton.ac.uk/id/eprint/54070
ISSN: 0264-9381
PURE UUID: 5fe5866a-19ce-4377-bcc4-3e06fd12051b
ORCID for Carsten Gundlach: ORCID iD orcid.org/0000-0001-9585-5375

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Date deposited: 28 Jul 2008
Last modified: 20 Jul 2018 00:34

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