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Black hole evolution by spectral methods

Lawrence E. Kidder·Mark A. Scheel·Saul A. Teukolsky·Eric D. Carlson·Gregory B. Cook
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Abstract

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.

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Lawrence E. Kidder, Mark A. Scheel, Saul A. Teukolsky, Eric D. Carlson, Gregory B. Cook. 2000-05-15. Black hole evolution by spectral methods. https://doi.org/10.1103/physrevd.62.084032

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