Generalized Harmonic Equations in 3+1 Form

Details Generalized Harmonic Equations in 3+1 Form Generalized Harmonic Equations in 3+1 Form

2011-09-08

arxiv.org/abs/1109.1707v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

This version (accepted for publication) contains some minor corrections and additional references

Scientific paper

The generalized harmonic equations of general relativity are written in 3+1 form. The result is a system of partial differential equations with first order time and second order space derivatives for the spatial metric, extrinsic curvature, lapse function and shift vector, plus fields that represent the time derivatives of the lapse and shift. This allows for a direct comparison between the generalized harmonic and the Arnowitt-Deser-Misner formulations. The 3+1 generalized harmonic equations are also written in terms of conformal variables and compared to the Baumgarte-Shapiro-Shibata-Nakamura equations with moving puncture gauge conditions.

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