Twistor Theory of Higher-Dimensional Black Holes - Part I: Theory

The correspondence between stationary, axisymmetric, asymptotically flat space-times and bundles over a reduced twistor space has been established in four dimensions. The main impediment for an application of this correspondence to examples in higher dimensions has been the lack of a higher-dimensional equivalent of the Ernst potential. This article will propose such a generalized Ernst potential, point out where the rod structure of the space-time can be found in the twistor picture and thereby provide a procedure for generating solutions to the Einstein equations in higher dimensions from the rod structure and other asymptotic data. An important result for the study of five-dimensional examples will be the theorem which relates the patching matrices on the outer semi-infinite rods.