A spectral approach to the Dirac equation in the non-extreme Kerr–Newmann metric

Abstract

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