  The causal properties of the family of Kerr-de Sitter spacetimes are analyzed
and compared to those of the Kerr family. At first we show that a Kerr-de
Sitter spacetime can be viewed as an assembly of Carter's blocks i.e. four
dimensional spacetime regions contained within Killing horizons or a Killing
horizon and the asymptotic de Sitter region. From this perspective and leaving
aside topological identifications, the causal properties of a Kerr de Sitter
spacetime are determined by the causal properties of the individual Carter's
blocks viewed as spacetimes in their own right. We show that any Carter's block
is stably causal except for the blocks that contain the ring singularity. The
latter are vicious sets: any two events within such block can be connected by a
future (respectively past) directed timelike curve. This behavior is identical
to the causal behavior of the Boyer-Lindquist blocks that contains the Kerr
ring singularity which are also vicious sets. On the other hand, while for the
case of a naked Kerr singularity the entire spacetime is a vicious set and thus
closed timelike curves pass through any event including events lying in the
asymptotic region, for the case of a Kerr-de Sitter spacetime the cosmological
horizons imply that the asymptotic de Sitter region is causally well behaved.
In that regard a positive cosmological constant appears to improve the causal
behavior of the underlying spacetime.
