Sharp Asymptotics for Einstein- \({\lambda}\) -Dust Flows

详细信息    查看全文

• 作者：Helmut Friedrich
• 刊名：Communications in Mathematical Physics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：350
• 期：2
• 页码：803-844
• 全文大小：739KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0916
• 卷排序：350

文摘

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 which develop into solutions that admit at future time-like infinity a space-like conformal boundary \({{\mathcal J}^+}\) that is \({C^{\infty}}\) if the data are of class \({C^{\infty}}\) 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 \({{\mathcal J}^+}\). 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.