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Constraint damping in the Z4 formulation and harmonic gauge

Constraint damping in the Z4 formulation and harmonic gauge
Constraint damping in the Z4 formulation and harmonic gauge
We show that by adding suitable lower-order terms to the Z4 formulation of the Einstein equations, all constraint violations except constant modes are damped. This makes the Z4 formulation a particularly simple example of a ?-system as suggested by Brodbeck et al (1999 J. Math. Phys. 40 909). We also show that the Einstein equations in harmonic coordinates can be obtained from the Z4 formulation by a change of variables that leaves the implied constraint evolution system unchanged. Therefore, the same method can be used to damp all constraints in the Einstein equations in harmonic gauge.
0264-9381
3767-3773
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Hinder, Ian
a417f53a-afd7-49ca-8c2b-b4c055ec44a0
Martin-Garcia, José M.
98ce3629-0c09-4223-8098-40e64b22b837
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Hinder, Ian
a417f53a-afd7-49ca-8c2b-b4c055ec44a0
Martin-Garcia, José M.
98ce3629-0c09-4223-8098-40e64b22b837

Gundlach, Carsten, Calabrese, Gioel, Hinder, Ian and Martin-Garcia, José M. (2005) Constraint damping in the Z4 formulation and harmonic gauge. Classical and Quantum Gravity, 22 (17), 3767-3773. (doi:10.1088/0264-9381/22/17/025).

Record type: Article

Abstract

We show that by adding suitable lower-order terms to the Z4 formulation of the Einstein equations, all constraint violations except constant modes are damped. This makes the Z4 formulation a particularly simple example of a ?-system as suggested by Brodbeck et al (1999 J. Math. Phys. 40 909). We also show that the Einstein equations in harmonic coordinates can be obtained from the Z4 formulation by a change of variables that leaves the implied constraint evolution system unchanged. Therefore, the same method can be used to damp all constraints in the Einstein equations in harmonic gauge.

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Published date: September 2005

Identifiers

Local EPrints ID: 29200
URI: https://eprints.soton.ac.uk/id/eprint/29200
ISSN: 0264-9381
PURE UUID: 181b181a-17b9-4f39-9337-87a82ea9ce36
ORCID for Carsten Gundlach: ORCID iD orcid.org/0000-0001-9585-5375

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Date deposited: 11 May 2006
Last modified: 20 Jul 2018 00:34

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