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Sharp asymptotics for Einstein-lambda-dust flows

Friedrich, H. (2017). Sharp asymptotics for Einstein-lambda-dust flows. Communications in Mathematical Physics, 350(2), 803-844. doi:10.1007/s00220-016-2716-6.

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Creators:
Friedrich, Helmut1, Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,
Abstract: We consider the Einstein-dust equations with positive cosmological constant $\lambda$ on manifolds with time slices diffeomorphic to an orientable, compact 3-manifold $S$. It is shown that the set of standard Cauchy data for the Einstein-$\lambda$-dust equations on $S$ contains an open (in terms of suitable Sobolev norms) subset of data that develop into solutions which admit at future time-like infinity a space-like conformal boundary ${\cal J}^+$ that is $C^{\infty}$ if the data are of class $C^{\infty}$ and of correspondingly lower smoothness otherwise. As a particular case follows a strong stability result for FLRW solutions. The solutions can conveniently be characterized in terms of their asymptotic end data induced on ${\cal J}^+$, only a linear equation must be solved to construct such data. In the case where the energy density $\hat{\rho}$ is everywhere positive such data can be constructed without solving any differential equation at all.

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Dates: 2016-01-1820162017
Publication Status: Published in print
Pages: 44 pages
Publishing info: -
Rev. Method: -
Identifiers: arXiv: 1601.04506
URI: http://arxiv.org/abs/1601.04506
DOI: 10.1007/s00220-016-2716-6
Degree: -

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Title: Communications in Mathematical Physics
Source Genre: Journal
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Publ. Info: Heidelberg : Springer-Verlag Heidelberg
Pages: - Volume / Issue: 350 (2) Sequence Number: - Start / End Page: 803 - 844 Identifier: ISSN: 0010-3616
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/954925392313