Boundary conditions in linearized harmonic gravity
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.
Keywords
Cite
@article{arxiv.gr-qc/0106026,
title = {Boundary conditions in linearized harmonic gravity},
author = {Bela Szilagyi and Bernd Schmidt and Jeffrey Winicour},
journal= {arXiv preprint arXiv:gr-qc/0106026},
year = {2011}
}
Comments
22 pages, 6 Postscript figures