Nonexistence of time-periodic solutions of the Dirac equation in nonextreme Kerr-Newman-AdS spacetime

In non-extreme Kerr-Newman-AdS spacetime, we prove that there is no nontrivial Dirac particle which is $L^p$ for $0<p\le \frac{4}{3}$ with arbitrary eigenvalue $\lambda$, and for $\frac{4}{3}<p\le \frac{4}{3-2q}$, $0<q<\frac{3}{2}$ with eigenvalue $\mathrm{\mid }\lambda \mathrm{\mid }>q\kappa$, outside and away from the event horizon. By taking $q=\frac{1}{2}$, we show that there is no normalizable massive Dirac particle with mass greater than $\frac{\kappa }{2}$ outside and away from the event horizon in non-extreme Kerr-Newman-AdS spacetime, and they must either disappear into the black hole or escape to infinity, and this recovers the same result of Belgiorno and Cacciatori in the case of $Q=0$ obtained by using spectral methods. Furthermore, we prove that any Dirac particle with eigenvalue $\mathrm{\mid }\lambda \mathrm{\mid }<\frac{\kappa }{2}$ must be $L^2$ outside and away from the event horizon.