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Journal Article

Cauchy boundaries in linearized gravitational theory

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

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

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Phy.Rev.D.62.104006.pdf
(Publisher version), 123KB

9912030v2.pdf
(Preprint), 226KB

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Citation

Szilagyi, B., Gomez, R., Bishop, N. T., & Winicour, J. (2000). Cauchy boundaries in linearized gravitational theory. Physical Review D, 62(10): 104006. doi:10.1103/PhysRevD.62.104006.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-56F3-7
Abstract
We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a three-dimensional bounded domain. Criteria of robust stability are proposed, developed into a testbed and used to study various evolution-boundary algorithms. We construct a standard explicit finite difference code which solves the unconstrained linearized Einstein equations in the 3 + 1 formulation and measure its stability properties under Dirichlet, Neumann, and Sommerfeld boundary conditions. We demonstrate the robust stability of a specific evolution-boundary algorithm under random constraint violating initial data and random boundary data.