Twistor theory of higher-dimensional black holes

Thesis

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 poten- tial. 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.

Authors: Metzner, N

• Publication date: 2012
• DOI: 10.5287/ora-n6rdra16o
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: myers perry black hole; black holes; ernst potential; twistor theory; penrose ward transform; reduced twistor space; conical singularity; higher dimensions; black ring
• Subjects: Relativity and gravitational theory (mathematics)