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Cauchy boundaries in linearized gravitational theory

Bela Szilagyi·Roberto Gomez·Nigel T. Bishop·Jeffrey Winicour
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Abstract

We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a 3-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.

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Bela Szilagyi, Roberto Gomez, Nigel T. Bishop, Jeffrey Winicour. 2000-12-31. Cauchy boundaries in linearized gravitational theory. https://doi.org/10.1103/physrevd.62.104006

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