We show that in D=2n+1 dimensions, when mass is negative and all angular momenta are non-vanishing, Kerr and Kerr-AdS metrics describe smooth time machines, with no curvature singularity. Turning off the angular momenta appropriately can lead to static AdS solitons with negative mass. Setting zero the cosmological constant yields a class of Ricci-flat Kähler metrics in D=2n dimensions. We also show that Euclidean-signatured AdS solitons with negative mass can also arise in odd dimensions. We then construct time machines in D=5 minimal gauged supergravity that carry only magnetic dipole charges. Turning off the cosmological constant, the time machine becomes massless and asymptotically flat. It can be described as a constant time bundle over the Eguchi-Hanson instanton.

Latex, 32 pages