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Stability of Black Holes
PDE Seminar| Speaker: | Joel Smoller, Michigan |
| Location: | 3106 MSB |
| Start time: | Wed, May 2 2007, 4:10PM |
We consider decay of solutions of the Cauchy Problem for various fields in the Kerr (rotating Black Hole) geometry. We discuss the formulation of the problem in terms of the Teukolsky equation, a single second-order PDE depending on a real parameter s, the "spin". For various values of s, the Teukolsky equation describes different fields in the Kerr geometry: s=0,1/2,1, 2, correspond, respectively, to scalar waves, Dirac's equations, Maxwell's equations, and gravitational waves. We discuss our results for s=0,1/2, as well as our rigorous proof of Penrose's proposal (1969) for energy extraction from a Kerr BH. In the case of a Schwarzschild (non-rotating) BH, we discuss our decay results, and hence stability of this BH, for all spin.