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  A global foliation of Einstein-Euler spacetimes with Gowdy symmetry on T^3

LeFloch, P. G., & Rendall, A. D. (2011). A global foliation of Einstein-Euler spacetimes with Gowdy symmetry on T^3. Archive for Rational Mechanics and Analysis, 201(3), 841-870. doi:10.1007/s00205-011-0425-z.

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LeFloch, P. G., Author
Rendall, Alan D.1, Author           
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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 Abstract: We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T (3), and we construct matter spacetimes with low regularity. These spacetimes admit both impulsive gravitational waves in the metric (for instance, Dirac mass curvature singularities propagating at light speed) and shock waves in the fluid (that is, discontinuities propagating at about the sound speed). Given an initial data set, we establish the existence of a future development, and we provide a global foliation in terms of a globally and geometrically defined time-function, closely related to the area of the orbits of the symmetry group. The main difficulty lies in the low regularity assumed on the initial data set which requires a distributional formulation of the Einstein-Euler equations.

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 Dates: 2010-03-24201020112011
 Publication Status: Issued
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 Identifiers: arXiv: 1004.0427
DOI: 10.1007/s00205-011-0425-z
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Title: Archive for Rational Mechanics and Analysis
Source Genre: Journal
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Publ. Info: Berlin : Springer-Verlag
Pages: - Volume / Issue: 201 (3) Sequence Number: - Start / End Page: 841 - 870 Identifier: ISSN: 0003-9527
CoNE: https://pure.mpg.de/cone/journals/resource/954925381021