Twistor Theory of Higher-Dimensional Black Holes

TL;DR

This paper extends twistor theory to higher-dimensional black holes by proposing a generalized Ernst potential, enabling solution generation from rod structures and asymptotic data, with applications demonstrated in five dimensions.

Contribution

It introduces a higher-dimensional Ernst potential and a method to generate solutions using twistor theory, addressing previous limitations in higher-dimensional cases.

Findings

Developed rules for patching matrix transitions.

Provided procedures to eliminate conical singularities.

Applied methods to five-dimensional black hole examples.

Abstract

The correspondence of 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 is the lack of a higher-dimensional equivalent of the Ernst potential. This thesis 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 field equations in higher dimensions from the rod structure, other asymptotic data, and the requirement of a regular axis. Examples in five dimensions are studied and necessary tools are developed, in particular rules for the transition between different adaptations of the patching matrix and rules for the elimination of conical singularities.