Three Dimensional Numerical Relativity with a Hyperbolic Formulation
Abstract
We discuss a successful three-dimensional cartesian implementation of the Bona-Mass\'o hyperbolic formulation of the 3+1 Einstein evolution equations in numerical relativity. The numerical code, which we call ``Cactus,'' provides a general framework for 3D numerical relativity, and can include various formulations of the evolution equations, initial data sets, and analysis modules. We show important code tests, including dynamically sliced flat space, wave spacetimes, and black hole spacetimes. We discuss the numerical convergence of each spacetime, and also compare results with previously tested codes based on other formalisms, including the traditional ADM formalism. This is the first time that a hyperbolic reformulation of Einstein's equations has been shown appropriate for three-dimensional numerical relativity in a wide variety of spacetimes.
Keywords
Cite
@article{arxiv.gr-qc/9804052,
title = {Three Dimensional Numerical Relativity with a Hyperbolic Formulation},
author = {Carles Bona and Joan Masso and Edward Seidel and Paul Walker},
journal= {arXiv preprint arXiv:gr-qc/9804052},
year = {2007}
}
Comments
Corrected a wrong reference, added two, fixed notation and changed a figure. 35 double column pages including 41 figures. Version with higher quality figures, movies and more available at http://cactus.aei-potsdam.mpg.de