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

Abstract

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 $|\lambda |>q\kappa$, 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 $|\lambda |<\frac{\kappa }{2}$ must be $L^2$ outside and away from the event horizon.

14 pages. The electromagnetic vector potential A (page 2) is corrected, which revises the right expressions of D_{r\pm} (page 6), L_{θ\pm} (page 6), α_1 (page 6) and α_2 (page 7). It gives α_1 (page 9) is of o(1/r), and results all |λ|>|Q|+qκ, |Q|+κ/2, and λ<-|Q|-qκare changes to |λ|>qκ, κ/2, and λ<-qκrespectively

References in corpus (1)

• Non-Existence of Time-Periodic Solutions of the Dirac Equation in an Axisymmetric Black Hole Geometry