2004/04/30 by Jonathan Thornburg · 6 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Pulsars and Gravitational Waves Research #gr-qc
paper · pdf · doi:10.1088/0264-9381/21/15/004
published as Class.Quant.Grav. 21 (2004) 3665-3692 · 31 pages, revtex4, includes color postscript figures, mpeg movies available at http://www.aei.mpg.de/~jthorn/research/mpe/movies/, v4 = final version as published = v3 + correct acknowledgments + correct grid pars in table 1
openalex publication_date 2004/07/14 · arxiv created 2004/07/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When using black-hole excision to numerically evolve a black-hole spacetime with no continuous symmetries, most 3+1 finite differencing codes use a Cartesian grid. It is difficult to do excision on such a grid because the natural r = constant excision surface must be approximated either by a very different shape such as a contained cube, or by an irregular and non-smooth 'LEGO1 sphere' which may introduce numerical instabilities into the evolution. In this paper I describe an alternate scheme which uses multiple r × (angular coordinates) patches, each patch using a different (nonsingular) choice of angular coordinates. This allows excision on a smooth r = constant 2-sphere. I discuss the key design choices in such a multiple-patch scheme, including the choice of ghost-zone versus internal-boundary treatment of the interpatch boundaries (I use a ghost-zone scheme), the number and shape of the patches (I use a 6-patch 'inflated-cube' scheme), the details of how the ghost zones are 'synchronized' by interpolation from neighbouring patches, the tensor basis for the Einstein equations in each patch, and the handling of non-tensor field variables such as the BSSN Γ<sup>~i</sup> (I use a scheme which requires ghost zones which are twice as wide for the BSSN conformal factor φ as for Γ<sup>~i</sup> and the other BSSN field variables). I present sample numerical results from a prototype implementation of this scheme. This code simulates the time evolution of the (asymptotically flat) spacetime around a single (excised) black hole, using fourth-order finite differencing in space and time. Using Kerr initial data with J/m<sup>2</sup> = 0.6, I present evolutions to t &gt;~ 1500m. The lifetime of these evolutions appears to be limited only by outer boundary instabilities, not by any excision instabilities or by any problems inherent to the multiple-patch scheme.