Abstract
We present a technique that can be used to generate a static, axisymmetric solution of the Einstein-Maxwell-dilaton equations from a stationary, axisymmetric solution of the vacuum Einstein equations. Starting from the Kerr solution, Davidson and Gedalin have previously made use of this technique to obtain a pair of oppositely charged, extremal dilatonic black holes, known as a black dihole. In this paper, we shall instead start from the Kerr-NUT (Newman-Unti-Tamburino) solution. It will be shown that the new solution can also be interpreted as a dihole, but with the black holes carrying unbalanced magnetic charges. The effect of the NUT parameter is to introduce a net magnetic charge into the system. Finally, we uplift our solution to ten dimensions to describe a system consisting of $D6$ and anti--$D6$-branes with unbalanced charges. The limit in which they coincide agrees with a solution recently derived by Brax et al.
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