Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-08-04
Phys.Rev.D82:124010,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Revised version, includes explicit expresions for gauge sources corresponding to 1+log and gamma-driver gauge conditions ('pun
Scientific paper
10.1103/PhysRevD.82.124010
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 $Z_\mu = 0$ 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.
Bona Carles
Bona-Casas Carles
Palenzuela Carlos
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