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.

4829-4845

Calabrese, Gioel

b6d18b27-64cd-426f-b86e-1b3a848f03ed

Gundlach, Carsten

586f1eb5-3185-4b2b-8656-c29c436040fc

Hilditch, David

108ec927-5127-4228-86d5-493291f22021

July 2006

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, .
(doi:10.1088/0264-9381/23/15/004).

## 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

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Date deposited: 28 Jul 2008

Last modified: 20 Jul 2018 00:34

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## Contributors

Author:
Gioel Calabrese

Author:
David Hilditch

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