Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-07-02
Phys.Rev. D70 (2004) 084017
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
final version with minor changes; 16 pages, 14 figures
Scientific paper
10.1103/PhysRevD.70.084017
Techniques are developed for projecting the solutions of symmetric hyperbolic evolution systems onto the constraint submanifold (the constraint-satisfying subset of the dynamical field space). These optimal projections map a field configuration to the ``nearest'' configuration in the constraint submanifold, where distances between configurations are measured with the natural metric on the space of dynamical fields. The construction and use of these projections is illustrated for a new representation of the scalar field equation that exhibits both bulk and boundary generated constraint violations. Numerical simulations on a black-hole background show that bulk constraint violations cannot be controlled by constraint-preserving boundary conditions alone, but are effectively controlled by constraint projection. Simulations also show that constraint violations entering through boundaries cannot be controlled by constraint projection alone, but are controlled by constraint-preserving boundary conditions. Numerical solutions to the pathological scalar field system are shown to converge to solutions of a standard representation of the scalar field equation when constraint projection and constraint-preserving boundary conditions are used together.
Holst Michael
Kidder Lawrence E.
Lindblom Lee
Owen Robert
Pfeiffer Harald P.
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