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  The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes

Barnes, A. P., Lefloch, P. G., Schmidt, B. G., & Stewart, J. M. (2004). The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes. Classical and Quantum Gravity, 21, 5043-5074. Retrieved from http://www.iop.org/EJ/article/0264-9381/21/22/003/cqg4_22_003.pdf.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4FCE-7 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4FCF-5
Genre: Journal Article

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cqg4_22_003.pdf (Publisher version), 462KB
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 Creators:
Barnes, A. P., Author
Lefloch, P. G., Author
Schmidt, Bernd G.1, Author
Stewart, J. M., Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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 Abstract: We propose a new, augmented formulation of the coupled Euler–Einstein equations for perfect fluids on plane-symmetric Gowdy spacetimes. The unknowns of the augmented system are the density and velocity of the fluid and the first- and second-order spacetime derivatives of the metric. We solve the Riemann problem for the augmented system, allowing propagating discontinuities in both the fluid variables and the first- and second-order derivatives of the geometry coefficients. Our main result, based on Glimm's random choice scheme, is the existence of solutions with bounded total variation of the Euler–Einstein equations, up to the first time where a blow-up singularity (unbounded first-order derivatives of the geometry coefficients) occurs. We demonstrate the relevance of the augmented system for numerical relativity. We also consider general vacuum spacetimes and solve a Riemann problem, by relying on a theorem by Rendall on the characteristic value problem for the Einstein equations.

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Language(s): eng - English
 Dates: 2004-10-20
 Publication Status: Published in print
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Title: Classical and Quantum Gravity
Source Genre: Journal
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Pages: - Volume / Issue: 21 Sequence Number: - Start / End Page: 5043 - 5074 Identifier: -