Causal properties of AdS-isometry groups I: Causal actions and limit sets

dc.creatorBarbot, Thierry
dc.date2005-09-23
dc.date2006-02-07
dc.date.accessioned2026-07-07T09:30:34Z
dc.date.available2026-07-07T09:30:34Z
dc.descriptionWe study the causality relation in the 3-dimensional anti-de Sitter space AdS and its conformal boundary Ein. To any closed achronal subset $Λ$ in ${Ein}\_2$ we associate the invisible domain $E(Λ)$ from $Λ$ in AdS. We show that if $Γ$ is a torsion-free discrete group of isometries of AdS preserving $Λ$ and is non-elementary (for example, not abelian) then the action of $Γ$ on $E(Λ)$ is free, properly discontinuous and strongly causal. If $Λ$ is a topological circle then the quotient space $M\_Λ(Γ) = Γ\backslash{E}(Λ)$ 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 $Γ$ 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.
dc.identifierhttps://arxiv.org/abs/math/0509552
dc.identifierhttp://arxiv.org/abs/math/0509552
dc.identifierAdv. Theor. Math. Phys. 12, 1 (2008) 1--66
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158161
dc.subjectGeometric Topology
dc.subject53C50, 57M50, 57S30
dc.titleCausal properties of AdS-isometry groups I: Causal actions and limit sets
dc.typetext

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