Black diholes with unbalanced magnetic charges

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 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..