Causal properties of AdS-isometry groups I: Causal actions and limit sets
Causal properties of AdS-isometry groups I: Causal actions and limit sets
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AdS 等距组 I 的因果属性：因果行为和极限集
DOI：
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发表时间：
2005
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通讯作者：
Thierry Barbot
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作者：
Thierry Barbot
研究了$3$维反德西特空间AdS及其共形边界$mbox{Ein}_2$中的因果关系。对于$mbox{Ein}_2$中的任意闭合无历时子集$Lambda$，我们将ad中的$Lambda$关联为不可见域$E(Lambda)$。我们证明了如果$Gamma$是保留$Lambda$的ad的无扭等距离散群，并且是非初等的（例如，非阿贝），则$Gamma$对$E(Lambda)$的作用是自由的、适当不连续的和强因果的。如果$Lambda$是一个拓扑圆，则商空间$M_Lambda(Gamma) = Gammaackslash{E}(Lambda)$是一个允许柯西曲面$S$的极大全局双曲ads -时空，使得$S$上的诱导度规是完备的。在即将发表的一篇论文中，我们研究了$Gamma$为初等的情况，并利用本文的结果定义了一个包含所有已知BTZ多重黑洞的ads -时空大族。
We study the causality relation in the $3$-dimensional anti-de Sitter space AdS and its conformal boundary $mbox{Ein}_2$. To any closed achronal subset $Lambda$ in $mbox{Ein}_2$ we associate the invisible domain $E(Lambda)$ from $Lambda$ in AdS. We show that if $Gamma$ is a torsion-free discrete group of isometries of AdS preserving $Lambda$ and is non-elementary (for example, not abelian) then the action of $Gamma$ on $E(Lambda)$ is free, properly discontinuous and strongly causal. If $Lambda$ is a topological circle then the quotient space $M_Lambda(Gamma) = Gammaackslash{E}(Lambda)$ is a maximal globally hyperbolic AdS-spacetime admitting a Cauchy surface $S$ such that the induced metric on $S$ is complete. In a forthcoming paper we study the case where $Gamma$ is elementary and use the results of the present paper to define a large family of AdS-spacetimes including all the previously known examples of BTZ multi-black holes.