2012/01/01 by Norman Metzner, Metzner, Norman
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Relativity and Gravitational Theory #gr-qc #math-ph #math.DG #math.MP
paper · pdf · doi:10.48550/arxiv.1207.0115
DPhil Thesis (University of Oxford, submitted February 2012), 119 pages, 15 figures
openalex publication_date 2012/01/01 · arxiv created 2012/06/30 · arxiv updated 2012/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.