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Constraint damping in the Z4 formulation and harmonic gauge

Carsten Gundlach·Jose M. Martin-Garcia·Gioel Calabrese·Ian Hinder
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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 lambda-system as suggested by Brodbeck et al. 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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Carsten Gundlach, Jose M. Martin-Garcia, Gioel Calabrese, Ian Hinder. 2005-07-14. Constraint damping in the Z4 formulation and harmonic gauge. https://doi.org/10.1088/0264-9381%2F22%2F17%2F025

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