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

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 $\mu \ge \frac{1}{2l}$ 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.

27 pages, AMS style. Some misprints corrected. Improvements in sections 1,5 and 6 and in Appendix A (improved discussion of the Dirac quantization condition). References added

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• The Dirac system on the Anti-de Sitter Universe
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• The Dirac propagator in the Kerr-Newman metric
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• Greybody Radiation of scalar and Dirac perturbations of NUT Black Holes
• Slowly damped quasinormal modes of the massive Dirac field in d-dimensional Tangherlini spacetime
• Dirac equation in Kerr-Taub NUT spacetime
• Analysis of half-spin particle motion in Kerr-Newman field by means of effective potentials in second-order equations
• The Dirac point electron in zero-gravity Kerr--Newman spacetime
• The Dirac equation in Schwarzschild mass coupled to a Stationary Electromagnetic Field
• Stationary solutions of the second-order equation for fermions in Kerr-Newman space-time
• Quantum properties of the Dirac field on BTZ black hole backgrounds
• Zero, Normal and Super-radiant Modes for Scalar and Spinor Fields in Kerr-anti de Sitter Spacetime