标题： Kerr-de Sitter时空无限角动量参数的极限 $a$ 显示英文标题

标题： The limit of Kerr-de Sitter spacetime with infinite angular-momentum parameter $a$

摘要： 我们考虑Kerr-de Sitter时空的极限$a\rightarrow \infty$。 该时空是真空爱因斯坦场方程在正宇宙常数$\Lambda$下的Petrov类型-D解，马尔斯-西蒙张量为零且符合平坦的scri。 它具有一个阿贝尔的二维对称群，其轨道在不同区域为类空或类时，且作为特殊情况包括de Sitter时空。 详细分析了该解的全局结构，特别关注其Killing视界：它们由有限面积的非紧致准零测表面构成，其中一个“接触”曲率奇点，该奇点类似于一个类光的二维表面。 在这两个视界之间的区域之外存在再次为非紧致的零测表面。 除了$\Lambda$外，该解包含一个唯一的自由参数，可以以精确的方式与非奇异视界的角动量相关联。 显式构建了时空（轴）的最大延拓。 我们还分析了scri的结构，其拓扑为$\mathbb{R}^3$。 显示英文摘要

摘要： We consider the limit $a\rightarrow \infty$ of the Kerr-de Sitter spacetime. The spacetime is a Petrov type-D solution of the vacuum Einstein field equations with a positive cosmological constant $\Lambda$, vanishing Mars-Simon tensor and conformally flat scri. It possesses an Abelian 2-dimensional group of symmetries whose orbits are spacelike or timelike in different regions, and it includes, as a particular case, de Sitter spacetime. The global structure of the solution is analyzed in detail, with particular attention to its Killing horizons: they are foliated by non-compact marginally trapped surfaces of finite area, and one of them `touches' the curvature singularity, which resembles a null 2-dimensional surface. Outside the region between these horizons there exist trapped surfaces that again are non-compact. The solution contains, apart from $\Lambda$, a unique free parameter which can be related to the angular momentum of the non-singular horizon in a precise way. A maximal extension of the (axis of the) spacetime is explicitly built. We also analyze the structure of scri, whose topology is $\mathbb{R}^3$.