  The geodesics of the rotating extreme black hole in five spacetime dimensions
found by Breckenridge, Myers, Peet and Vafa are Liouville integrable and may be
integrated by additively separating the Hamilton-Jacobi equation. This allows
us to obtain the St\"ackel-Killing tensor. We use these facts to give the
maximal analytic extension of the spacetime and discuss some aspects of its
causal structure. In particular, we exhibit a `repulson'-like behaviour
occuring when there are naked closed timelike curves. In this case we find that
the spacetime is geodesically complete (with respect to causal geodesics) and
free of singularities. When a partial Cauchy surface exists, we show, by
solving the Klein-Gordon equation, that the absorption cross-section for
massless waves at small frequencies is given by the area of the hole. At high
frequencies a dependence on the angular quantum numbers of the wave develops.
We comment on some aspects of `inertial time travel' and argue that such time
machines cannot be constructed by spinning up a black hole with no naked closed
timelike curves.
