Causal properties of AdS-isometry groups II: BTZ multi black-holes

This paper is the continuation of [8]. We essentially prove that the familly of strongly causal spacetimes defined in [8] associated to generic achronal subsets in Ein contains all the examples of BTZ multi black-holes. It provides new elements for the global description of these multi black-holes. We also prove that any strongly causal spacetime locally modelled on the anti-de Sitter space admits a well-defined maximal strongly causal conformal boundary locally modelled on Ein.