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We investigate the local energy decay of solutions of the Dirac equation inthe non-extreme Kerr-Newman metric. First, we write the Dirac equation as aCauchy problem and define the Dirac operator. It is shown that the Diracoperator is selfadjoint in a suitable Hilbert space. With the RAGE theorem, weshow that for each particle its energy located in any compact region outside ofthe event horizon of the Kerr-Newman black hole decays in the time mean.

On the local energy decay of solutions of the Dirac equation in the non-extreme Kerr-Newman metric, I