Scheel, Mark A. and Baumgarte, Thomas W. and Cook, Gregory B. and Shapiro, Stuart L. and Teukolsky, Saul A. (1997) Numerical evolution of black holes with a hyperbolic formulation of general relativity. Physical Review D, 56 (10). pp. 6320-6335. ISSN 2470-0010. doi:10.1103/PhysRevD.56.6320. https://resolver.caltech.edu/CaltechAUTHORS:20180629-155912237
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Abstract
We describe a numerical code that solves Einstein’s equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used to evolve a numerical spacetime containing a black hole. We excise the hole from the computational grid in order to avoid the central singularity. We describe in detail a causal differencing method that should allow one to stably evolve a hyperbolic system of equations in three spatial dimensions with an arbitrary shift vector, to second-order accuracy in both space and time. We demonstrate the success of this method in the spherically symmetric case.
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Additional Information: | © 1997 American Physical Society. (Received 19 June 1997) We thank Manish Parashar for his help with the DAGH system, and Andrew Abrahams, Charles Evans, Ed Seidel, Wai-Mo Suen, and James York for helpful discussions. This work was supported by the NSF Binary Black Hole Grand Challenge Grant No. NSF PHY 93-18152/ASC 93-18152 (ARPA supplemented), NSF Grant No. PHY 94-08378 at Cornell, and NSF Grant No. AST 96-18524 and NASA Grant No. NAG 5-3420 at Illinois. | ||||||||||||||
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Issue or Number: | 10 | ||||||||||||||
Classification Code: | PACS number(s): 04.25.Dm, 02.70.Bf, 04.70.Bw | ||||||||||||||
DOI: | 10.1103/PhysRevD.56.6320 | ||||||||||||||
Record Number: | CaltechAUTHORS:20180629-155912237 | ||||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180629-155912237 | ||||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||
ID Code: | 87500 | ||||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||||
Deposited By: | George Porter | ||||||||||||||
Deposited On: | 02 Jul 2018 14:55 | ||||||||||||||
Last Modified: | 15 Nov 2021 20:48 |
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