Quantum properties of the electron field in Kerr-Newman black hole manifolds

TL;DR

This paper analyzes the spectral properties of the electron Hamiltonian in Kerr-Newman black hole spacetimes, revealing a continuous spectrum with no gaps, which impacts black hole charge and angular momentum dissipation.

Contribution

It provides a detailed spectral analysis of the Dirac equation in Kerr-Newman backgrounds, showing the essential spectrum covers the entire real line and no discrete eigenvalues exist.

Findings

The essential spectrum of the Hamiltonian is the entire real line.

No spectral gaps or discrete eigenvalues are present for any black hole charge or angular momentum.

Spectral properties relate to black hole charge and angular momentum dissipation.

Abstract

We study some spectral features of the one-particle electron Hamiltonian obtained by separating the Dirac equation in a Kerr-Newman black hole background. We find that the essential spectrum includes the whole real line. As a consequence, there is no gap in the spectrum and discrete eigenvalues are not allowed for any value of the black hole charge $Q$ and angular momentum $J$. Our spectral analysis will be also related to the dissipation of the black hole angular momentum and charge.