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Treating instabilities in a hyperbolic formulation of Einstein’s equations

Scheel, Mark A. and Baumgarte, Thomas W. and Cook, Gregory B. and Shapiro, Stuart L. and Teukolsky, Saul A. (1998) Treating instabilities in a hyperbolic formulation of Einstein’s equations. Physical Review D, 58 (4). Art. No. 044020. ISSN 2470-0010. https://resolver.caltech.edu/CaltechAUTHORS:20180629-153601374

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Abstract

We have recently constructed a numerical code that evolves a spherically symmetric spacetime using a hyperbolic formulation of Einstein's equations. For the case of a Schwarzschild black hole, this code works well at early times, but quickly becomes inaccurate on a time scale of 10-100 M, where M is the mass of the hole. We present an analytic method that facilitates the detection of instabilities. Using this method, we identify a term in the evolution equations that leads to a rapidly-growing mode in the solution. After eliminating this term from the evolution equations by means of algebraic constraints, we can achieve free evolution for times exceeding 10000M. We discuss the implications for three-dimensional simulations.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevD.58.044020DOIArticle
http://arxiv.org/abs/gr-qc/9807029arXivDiscussion Paper
ORCID:
AuthorORCID
Teukolsky, Saul A.0000-0001-9765-4526
Additional Information:© 1998 American Physical Society. (Received 15 September 1997; published 27 July 1998) We thank Andrew Abrahams, Éanna Flanagan, Pablo Laguna, and James York for helpful discussions. This work was supported by the NSF Binary Black Hole Grand Challenge Grants Nos. NSF PHY 93-18152 and 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. Some computations were performed on the Cornell Theory Center SP2 and on the National Center for Supercomputing Applications SGI Origin 2000.
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:4
Classification Code:PACS number(s): 04.25.Dm, 02.60.Cb, 02.70.-c, 04.20.Ex
Record Number:CaltechAUTHORS:20180629-153601374
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180629-153601374
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87495
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:03 Jul 2018 16:33
Last Modified:22 Nov 2019 09:58

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