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Journal Article

Boundary conditions in linearized harmonic gravity

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Szilagyi,  Bela
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Schmidt,  Bernd
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Winicour,  Jeffrey
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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(Preprint), 358KB

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Citation

Szilagyi, B., Schmidt, B., & Winicour, J. (2002). Boundary conditions in linearized harmonic gravity. Physical Review D, 65: 064015.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-54F1-1
Abstract
We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a set of six wave equations. The results are used to formulate computational algorithms for Cauchy evolution in a 3-dimensional bounded domain. Numerical codes based upon these algorithms are shown to satisfy tests of robust stability for random constraint violating initial data and random boundary data; and shown to give excellent performance for the evolution of typical physical data. The results are obtained for plane boundaries as well as piecewise cubic spherical boundaries cut out of a Cartesian grid.