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arXiv · 1008.0747

Action principle for Numerical Relativity evolution systems

C. Bona·C. Bona-Casas·C. Palenzuela
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Abstract

A Lagrangian density is provided, that allows to recover the Z4 evolution system from an action principle. The resulting system is then strongly hyperbolic when supplemented by gauge conditions like '1+log' or 'freezing shift', suitable for numerical evolution. The physical constraint $Z_μ= 0$ can be imposed just on the initial data. The corresponding canonical equations are also provided. This opens the door to analogous results for other numerical-relativity formalisms, like BSSN, that can be derived from Z4 by a symmetry-breaking procedure. The harmonic formulation can be easily recovered by a slight modification of the procedure. This provides a mechanism for deriving both the field evolution equations and the gauge conditions from the action principle, with a view on using symplectic integrators for a constraint-preserving numerical evolution. The gauge sources corresponding to the 'puncture gauge' conditions are identified in this context.

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BibTeXRIS

C. Bona, C. Bona-Casas, C. Palenzuela. 2010-11-18. Action principle for Numerical Relativity evolution systems. https://doi.org/10.1103/physrevd.82.124010

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