Generalized Harmonic Equations in 3+1 Form
arXiv:1109.1707 · doi:10.1103/PhysRevD.84.124012
Abstract
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.
This version (accepted for publication) contains some minor corrections and additional references
References in corpus (10)
- Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4
- How to move a black hole without excision: gauge conditions for the numerical evolution of a moving puncture
- Simulations of Binary Black Hole Mergers Using Spectral Methods
- Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
- Covariant formulations of BSSN and the standard gauge
- An explicit harmonic code for black-hole evolution using excision
- Probing the puncture for black hole simulations
- Gauge Drivers for the Generalized Harmonic Einstein Equations
- Action principle for Numerical Relativity evolution systems
- Action Principle for the Generalized Harmonic Formulation of General Relativity