The Dirac Equation in Kerr-Newman-AdS Black Hole Background

TL;DR

This paper analyzes the Dirac equation in the Kerr-Newman-AdS black hole background, establishing selfadjointness of the Hamiltonian and showing the absence of bound states in the non-extremal case.

Contribution

It demonstrates the essential selfadjointness of the Dirac Hamiltonian in an asymptotically AdS black hole background and extends spectral analysis results to this setting.

Findings

Selfadjointness of the Dirac Hamiltonian is proven for massive fields.

No time-periodic, normalizable solutions exist in the non-extremal case.

Results align with known properties of asymptotically flat black holes.

Abstract

We consider the Dirac equation on the Kerr-Newman-AdS black hole background. We first perform the variable separation for the Dirac equation and define the Hamiltonian operator $\hat H$. Then we show that for a massive Dirac field with mass $\mu\geq \frac{1}{2l}$ essential selfadjointness of $\hat H$ on $C_0^{\infty} ((r_+,\infty) \times S^2)^4$ is obtained even in presence of the boundary-like behavior of infinity in an asymptotically AdS black hole background. Furthermore qualitative spectral properties of the Hamiltonian are taken into account and in agreement with the existing results concerning the case of stationary axi-symmetric asymptotically flat black holes we infer the absence of time-periodic and normalizable solutions of the Dirac equation around the black hole in the non-extremal case.