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The dimensional reduction of the bosonic sector of five-dimensional minimalsupergravity to a Lorentzian four-dimensional spacetime leads to a theory witha massless axion and a dilaton coupled to gravity and two U(1) gauge fields andthe dimensionally reduced equations of motion have SL(2,R)/SO(2)-dualityinvariance. In our previous work, utilizing the duality invariance, weformulated solution-generation techniques within five-dimensional minimalsupergravity. In this work, by choosing a timelike Killing vector, we considerdimensional reduction to a four-dimensional Euclidean space, in which the fieldequations have SL(2,R)/SO(1,1) invariance. In the timelike case, we develop anew duality transformation technique, while in the spacelike case we have donethat in the previous work. As an example, by applying it to the Rasheedsolutions, we obtain rotating Kaluza-Klein black hole solutions infive-dimensional minimal supergravity. In general, in contrast to the spacelikecase, the resulting dimensionally reduced solution includes the so-called NUTparameter and therefore from a four-dimensional point of view, such a spacetimeis not asymptotically flat. However, it is shown that in some special cases, itcan describe ordinary Kaluza-Klein black holes.

"Flip" of SL(2,R)-duality in five-dimensional supergravity