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The Long-Time Dynamics of Dirac Particles in the Kerr-Newman Black Hole Geometry
Felix Finster, Niky Kamran, Jan Smoller and Shing-Tung Yau
We consider the Cauchy problem for the massive Dirac equation in the non-extreme Kerr-Newman geometry outside the event horizon. We derive an integral representation for the Dirac propagator involving the solutions of the ODEs which arise in Chandrasekhar's separation of variables. It is proved that for initial data with compact support, the probability of the Dirac particle to be in any compact region of space tends to zero as t goes to infinity. This means that the Dirac particle must either disappear in the black hole or escape to spatial infinity. If the energy of the Dirac particle is strictly larger than its rest mass and its angular momentum is bounded, the Dirac wave function decays rapidly in t, locally uniformly in x.