Three Dimensional Numerical Relativity with a Hyperbolic Formulation

Abstract

We discuss a successful three-dimensional cartesian implementation of the Bona-Massó 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.

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

Cited by in corpus (7)

• Binary Black Hole Mergers in 3d Numerical Relativity
• Test-beds and applications for apparent horizon finders in numerical relativity
• Dirac's Observables for the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge
• GRaM-X: A new GPU-accelerated dynamical spacetime GRMHD code for Exascale computing with the Einstein Toolkit
• Numerical Relativity and Inhomogeneous Cosmologies
• Computational General Relativistic Force-Free Electrodynamics: I. Multi-Coordinate Implementation and Testing
• Orbifolds in Numerical Relativity