The seminar deals with topics related to gravitation and geometry,
including the following:
1) Gravitational Instantons - four-dimensional, complete, Ricci flat
manifolds with at least quadratic curvature decay. There are several
families of instantons, which all have special geometry. Solution
generating techniques, including the Belinski-Zakharov soliton method,
play an important role in constructing instantons. There are several
uniqueness conjectures for instantons that remain open.
2) Solitons - localized steady states of field theories. There is a
zoo of examples, in general relativity (eg. black holes, i.e. Lorentzian
versions of gravitational instantons), wave equations (eg. Q Balls),
Maxwell-Dirac theory, to name just a few. Surprisingly little is known
about the stability and dynamics of these objects in 3+1 dimensions.
- Kursleiter:in: Lars
- Kursleiter:in: Florian Hanisch