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arXiv · 1303.0850

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

Norman Metzner
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Abstract

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.

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Norman Metzner. 2013-03-04. Twistor Theory of Higher-Dimensional Black Holes - Part I: Theory. https://doi.org/10.1088/0264-9381/30/9/095001

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