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Boundary conditions in linearized harmonic gravity

Bela Szilagyi·Bernd Schmidt·Jeffrey Winicour
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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.

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Bela Szilagyi, Bernd Schmidt, Jeffrey Winicour. 2001-11-28. Boundary conditions in linearized harmonic gravity. https://doi.org/10.1103/physrevd.65.064015

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