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Numerical evolution of black holes with a hyperbolic formulation of general relativity

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. 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevD.56.6320DOIArticle
http://arxiv.org/abs/gr-qc/9708067arXivDiscussion Paper
ORCID:
AuthorORCID
Teukolsky, Saul A.0000-0001-9765-4526
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.
Funders:
Funding AgencyGrant Number
NSFPHY 93-18152
NSFASC 93-18152
Advanced Research Projects Agency (ARPA)UNSPECIFIED
NSFPHY 94-08378
NSFAST 96-18524
NASANAG 5-3420
Issue or Number:10
Classification Code:PACS number(s): 04.25.Dm, 02.70.Bf, 04.70.Bw
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:22 Nov 2019 09:58

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