Einstein 4-manifolds with two commuting Killing vectors (B06*)

• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 427320536

We will investigate the existence, rigidity and classification of 4-dimensional Lorentzian and Riemannian Einstein metrics with two commuting Killing vectors. Our goal is to address open questions in the study of black hole uniqueness and gravitational instantons. In the Ricci-flat case, the problem reduces to the analysis of axisymmetric harmonic maps from R^3 to the hyperbolic plane. In the case of negative Ricci curvature, a detailed understanding of the conformal boundary value problem for asymptotically hyperbolic Einstein metrics is required.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1442: Geometry: Deformations and Rigidity
• International Connection: United Kingdom
• Applicant Institution: Universität Münster
• Project Heads: Professor Dr. Hans-Joachim Hein, since 7/2024; Professor Dr. Gustav Holzegel, since 7/2024