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Black hole evolution by spectral methods

Kidder, Lawrence E. and Scheel, Mark A. and Teukolsky, Saul A. and Carlson, Eric D. and Cook, Gregory B. (2000) Black hole evolution by spectral methods. Physical Review D, 62 (8). Art. no. 084032. ISSN 2470-0010. https://resolver.caltech.edu/CaltechAUTHORS:20180605-153821098

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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 with 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevD.62.084032DOIArticle
https://arxiv.org/abs/gr-qc/0005056arXivDiscussion Paper
ORCID:
AuthorORCID
Kidder, Lawrence E.0000-0001-5392-7342
Teukolsky, Saul A.0000-0001-9765-4526
Additional Information:© 2000 American Physical Society. (Received 15 May 2000; published 26 September 2000) This work was supported in part by NSF grants PHY-9800737 and PHY-9900672 and NASA grant NAG5-7264 to Cornell University, and NSF grants PHY-9802571 and PHY-9988581 to Wake Forest University. Computations were performed on the National Computational Science Alliance SGI Origin2000, and on the Wake Forest University Department of Physics IBM SP2 with support from an IBM SUR grant.
Funders:
Funding AgencyGrant Number
NSFPHY-9800737
NSFPHY-9900672
NASANAG5-7264
NSFPHY-9802571
NSFPHY-9988581
IBMUNSPECIFIED
Issue or Number:8
Classification Code:PACS number(s): 04.25.Dm, 02.70.Hm
Record Number:CaltechAUTHORS:20180605-153821098
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180605-153821098
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86807
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:06 Jun 2018 15:12
Last Modified:09 Mar 2020 13:18

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