Black hole evolution by spectral methods
摘要
Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast to finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.
引用
@article{arxiv.gr-qc/0005056,
title = {Black hole evolution by spectral methods},
author = {Lawrence E. Kidder and Mark A. Scheel and Saul A. Teukolsky and Eric D. Carlson and Gregory B. Cook},
journal= {arXiv preprint arXiv:gr-qc/0005056},
year = {2009}
}
备注
20 pages, 17 figures, submitted to PRD