过去数年的各方面独立天文观测都表明当今的宇宙处于加速膨胀中。大量的观测结果都可以用带宇宙学常数的冷暗物质模型来解释。不仅如此，天文观测还表明，在几何单位制下宇宙学常数大小约为10^(-52)m^(-2)。在宇宙学尺度上，非零的宇宙学常数会影响时空的几何结构和对称性及对诸如引力波和电磁波的探测实验的分析和理解。但是，鉴于Einstein方程本身的复杂性，直接研究一般情形的时空结构十分困难，因此H.Bondi等人首先研究了渐近平坦时空的渐近结构和渐近对称性。本项目计划首先利用渐近展开的方法研究非零宇宙学常数且无物质场情况下时空的渐近结构，渐近对称群及其数学结构。在此过程中，还将进一步加深对Bondi所给的边界条件的理解。最后我们计划将结果推广到有电磁场的情况，并具体讨论宇宙学常数对引力场和电磁场性质的影响。

In the past years, people have found that our present universe is in a state of accelerated expansion from many independent astronomical observations. Most of the observations favor the cold dark matter model with a nonzero cosmological constant. Moreover, the observations show that the amplitude of the cosmological constant is about 10^(-52)m^(-2) in geometric units. On cosmological scale, the structure and symmetry of spacetime , the analysis and understanding of the experiments on gravitational waves and electromagnetic waves will be affected by the nonzero cosmological constant. On the other hand, due to the complexity of Eisntein’s equations, it is too difficult to investigate the structure of spacetime directly. So H.Bondi and other researchers began to discuss the asymptotic structure and asymptotic symmetries of asymptotically flat space in 1960s. This project plans to investigate the asymptotic structure and asymptotic symmetries of spacetime with nonzero cosmological constant but no material field by the method of asymptotic expansion firstly, the understanding on the meanings of Bondi type boundary condition will also be deepened in this process. Finally, the previous investigations will be generalized to the case with electromagnetic field, and the effect of cosmological constant on the properties of gravitational and electromagnetic field will also be discussed.