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  A conformal hyperbolic formulation of the Einstein equations.

Alcubierre, M., Brügmann, B., Miller, M., & Suen, W.-M. (1999). A conformal hyperbolic formulation of the Einstein equations. Physical Review D, 60(6): 064017. doi:10.1103/PhysRevD.60.064017.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-5864-C Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-5865-A
Genre: Journal Article

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PhyRevD60-1999-064017.pdf (Publisher version), 51KB
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 Creators:
Alcubierre, Miguel1, Author
Brügmann, Bernd1, Author
Miller, Mark, Author
Suen, Wai-Mo, Author
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1Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24013              

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 Abstract: We propose a reformulation of the Einstein evolution equations that cleanly separates the conformal degrees of freedom and the nonconformal degrees of freedom with the latter satisfying a first order strongly hyperbolic system. The conformal degrees of freedom are taken to be determined by the choice of slicing and the initial data, and are regarded as given functions (along with the lapse and the shift) in the hyperbolic part of the evolution. We find that there is a two parameter family of hyperbolic systems for the nonconformal degrees of freedom for a given set of trace free variables. The two parameters are uniquely fixed if we require the system to be “consistently trace-free,” i.e., the time derivatives of the trace free variables remain trace-free to the principal part, even in the presence of constraint violations due to numerical truncation error. We show that by forming linear combinations of the trace free variables a conformal hyperbolic system with only physical characteristic speeds can also be constructed.

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 Dates: 1999
 Publication Status: Issued
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 Identifiers: eDoc: 206101
Other: 16361
DOI: 10.1103/PhysRevD.60.064017
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Title: Physical Review D
Source Genre: Journal
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Pages: - Volume / Issue: 60 (6) Sequence Number: 064017 Start / End Page: - Identifier: ISSN: 1089-4918