The absence of normalizable time-periodic solutions for the Dirac equation in the Kerr–Newman–dS black hole background

Abstract

We consider the Dirac equation on the background of a Kerr–Newman–de Sitter black hole. By performing variable separation, we show that no time-periodic and normalizable solution of the Dirac equation is allowed, which amounts to the absence of quantum bound states for the Dirac Hamiltonian. This conclusion holds true even for extremal black holes. With respect to previously considered cases, the novelty is represented by the presence, in addition to a black hole event horizon, of a cosmological (non-degenerate) event horizon, which is at the root of the possibility to draw a conclusion on the aforementioned topic in a straightforward way even in the extremal case.