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

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

2008-03-17

arxiv.org/abs/0803.2496v3

Physics

Mathematical Physics

27 pages, AMS style. Some misprints corrected. Improvements in sections 1,5 and 6 and in Appendix A (improved discussion of th

Scientific paper

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.

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