Five-dimensional null and time-like supersymmetric geometries

We show that there exist supersymmetric solutions of five-dimensional, pure, N = 1 supergravity such that the norm of the supersymmetric Killing vector, built out of the Killing spinor, is a real not-everywhere analytic function such that all its derivatives vanish at a point where the Killing vector field becomes null. The norm of the Killing vector field then is not an analytic function on a neighborhood around this point. We explicitly construct such solutions by using a multi-center Gibbons-Hawking base. Although many of these solutions have infinite charges, we find explicit examples with finite charges that asymptote to AdS(3) x S-2 and discuss their physical interpretation.