Sharp Asymptotics for Einstein-λ-Dust Flows
Sharp Asymptotics for Einstein-λ-Dust Flows
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DOI：
10.1007/s00220-016-2716-6
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发表时间：
2017-03-01
影响因子：
2.4
通讯作者：
Friedrich, Helmut
中科院分区：
文献类型：
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作者：
Friedrich, Helmut
本文研究了具有正宇宙学常数的爱因斯坦-尘埃方程。关于时间片同构于可定向紧致3-流形S的流形。它表明，一组标准的柯西数据的爱因斯坦λ-尘埃方程S包含一个开放的（在适当的Sobolev范数）子集的数据，发展成解决方案，承认在未来的类时无穷大的类空共形边界J（+）是C-无穷大，如果数据类C-无穷大和相应的较低的光滑性，否则。这里考虑的解决方案类包括FLRW解决方案的非线性扰动作为非常特殊的情况。它可以方便地用J（+）上诱导的渐近终止数据来刻画。这些数据必须只满足一个线性微分方程。如果能量密度处处为正，则它们可以在根本不解微分方程的情况下构造。
We consider the Einstein-dust equations with positive cosmological constant. 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 which develop into solutions that admit at future time-like infinity a space-like conformal boundary J(+) that is C-infinity if the data are of class C-infinity and of correspondingly lower smoothness otherwise. The class of solutions considered here comprises non-linear perturbations of FLRW solutions as very special cases. It can conveniently be characterized in terms of asymptotic end data induced on J(+). These data must only satisfy a linear differential equation. If the energy density is everywhere positive they can be constructed without solving differential equations at all.