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Sharp asymptotics for Einstein-lambda-dust flows

MPG-Autoren
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Friedrich,  Helmut
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Volltexte (frei zugänglich)

1601.04506.pdf
(Preprint), 413KB

CMP016-2716-6.pdf
(Verlagsversion), 572KB

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Zitation

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.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0029-AAC0-4
Zusammenfassung
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.