Action principle for numerical-relativity evolution systems

作者：Bona C^*; Bona Casas C; Palenzuela C

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2010, 82(12): 124010.

DOI：10.1103/PhysRevD.82.124010

A Lagrangian density is provided that allows the recovery of 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 (Baumgarte-Shapiro-Shibata-Nakamura), 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.

• 出版日期2010-12-6