论文标题
不断扩展的宇宙中自我磨碎的尘埃球的未来稳定性
Future stability of self-gravitating dust balls in an expanding universe
论文作者
论文摘要
我们考虑一个代表不断扩展的宇宙中自我磨碎的灰尘球的系统。已经证明，可以在无穷大的情况下开出这种系统的数据，并在不发展冲击或奇异性的情况下向后进化。在时空的渐近区域中，存在于爱因斯坦 - lambda-dust方程的最终解决方案。此外，我们发现，如果与宇宙常数相比，密度很小，则可以在标准的cauchy hypersurface上构建宇宙学解决方案，代表代表自我磨碎的灰尘球。此外，如果假定密度足够小，则该初始数据会导致未来的地理图完全解决方案，以实现Einstein-Lambda-dust方程，该方程承认无穷大的平滑形式延伸，可以被视为De Sitter SpaceTime的扰动。该分析中的主要技术工具是爱因斯坦 - 兰姆巴达粉尘的弗里德里希（Friedrichs）保形的爱因斯坦野外方程，该粉刺以量规为块，其中尘埃的流量被重塑为保形地理器。
We consider a system representing self-gravitating balls of dust in an expanding Universe. It is demonstrated that one can prescribe data for such a system at infinity and evolve it backward in time without the development of shocks or singularities. The resulting solution to the Einstein-lambda-dust equations exists for an infinite amount of time in the asymptotic region of the spacetime. Furthermore, we find that if the density is small compared to the Cosmological constant, then it is possible to construct Cosmological solutions to the Einstein constraint equations on a standard Cauchy hypersurface representing self-gravitating balls of dust. If, in addition, the density is assumed to be sufficiently small, then this initial data gives rise to a future geodesically complete solution to the Einstein-lambda-dust equations admitting a smooth conformal extension at infinity which can be regarded as a perturbation of de Sitter spacetime. The main technical tool in this analysis are Friedrichs conformal Einstein field equations for the Einstein-lambda-dust written in terms of a gauge in which the flow lines of the dust are recast as conformal geodesics.
