Niky Kamran - Non-existence of time-periodic or quasi-periodic solutions of the Dirac operator in stationary axisymmetric black hole geometries

We have recently proved that the Dirac equation does not admit time-periodic or quasi-periodic solutions in the maximal analytic extension of the non-extreme Kerr-Newman charged rotating black hole. These theorems indicate that in contrast with the classical case of charged massive particle orbits, a quantum mechanical Dirac particle must either fall into the black hole or escape to infinity. We will outline the proofs of these results in our talk. This is joint work with F. Finster, J. Smoller and S.-T. Yau.