Black hole evolution by spectral methods - art. no. 084032

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of the se instabilities may be due to the numerical method used, traditionally fin ite differencing. In this paper, we explore the use of a pseudospectral col location (PSC) method for the evolution of a spherically symmetric black ho le spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherical ly symmetric black hole spacetime forever without enforcing constraints, ev en if we add dynamics via a Klein-Gordon scalar field. We find that, in con trast with finite-differencing methods, black hole excision is a trivial op eration using PSC applied to a hyperbolic formulation of Einstein's equatio ns. We discuss the extension of this method to three spatial dimensions.