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GR: Fachverband Gravitation und Relativitätstheorie

GR 11: Hauptvorträge Schwarze Löcher und Felder (gemeinsam mit MP)

GR 11.4: Invited Talk

Wednesday, February 29, 2012, 18:15–18:45, ZHG 002

Bidifferential calculus and integrable PDEs in General Relativity — •Folkert Müller-Hoissen — Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstrasse 10, D-37073 Göttingen

The ``bidifferential calculus approach'' to integrable partial differential (and difference) equations allows to deduce substantial results, e.g. methods to generate exact solutions, on an abstract level. Once a ``bidifferential calculus formulation'' of some equation is at hand, these general results can be evaluated in the concrete case. A special result in this framework, with a surprisingly simple proof, has recently been shown (joint work with Aristophanes Dimakis and Nils Kanning) to reproduce in particular the multi-Kerr-NUT and multi-Demianski-Newman families of solutions of the Ernst equations, governing stationary axisymmetric vacuum and electrovacuum space-times in General Relativity. We present an introduction to the underlying structures and methods of bidifferential calculus, and delegate a more detailed discussion of the case of the Ernst equations to the talk by Nils Kanning at this meeting.