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

TL;DR

This paper proves that the Dirac equation in a Kerr-Newman-de Sitter black hole background admits no time-periodic, normalizable solutions, even in extremal cases, due to the presence of multiple horizons.

Contribution

It demonstrates the non-existence of such solutions in a complex black hole spacetime with a cosmological horizon, extending previous results to extremal cases.

Findings

No time-periodic, normalizable solutions exist for the Dirac equation in this background.

The presence of a cosmological horizon is key to the non-existence proof.

Results hold even for extremal black hole configurations.

Abstract

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.