Absence of Normalizable Time-periodic Solutions for The Dirac Equation in Kerr-Newman-dS Black Hole Background

Understand

We consider the Dirac equation on the background of a Kerr-Newman-de Sitter black hole.

• By performing variable separation, we show that there exists no time-periodic and normalizable solution of the Dirac equation.
• This conclusion holds true even in the extremal case.
• With respect to previously considered cases, the novelty is represented by the presence, together with 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.