Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-05-15
Phys.Rev. D62 (2000) 084032
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
20 pages, 17 figures, submitted to PRD
Scientific paper
10.1103/PhysRevD.62.084032
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.
Carlson Eric D.
Cook Gregory B.
Kidder Lawrence E.
Scheel Mark A.
Teukolsky Saul A.
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