- Date de réalisation : 2 Juillet 2014
- Durée du programme : 60 min
- Classification Dewey : Mathématiques
- Auteur(s) : Andersson Lars
Dans la même collectionT. Ozuch - Noncollapsed degeneration and desingularization of Einstein 4-manifolds R. Perales - Recent Intrinsic Flat Convergence Theorems R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions A. Mondino - Time-like Ricci curvature bounds via optimal transport D. Semola - Boundary regularity and stability under lower Ricci bounds C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
Lars Andersson - Symmetry operators and energies
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin.