Monika Winklmeier, Osanobu Yamada
Spectral Analysis of Radial Dirac Operators in the Kerr-Newman Metric and its Applications to Time-periodic Solutions
(60K, latex)
ABSTRACT. We investigate the existence of time-periodic solutions of the Dirac equation in the Kerr-Newman background metric.
To this end, the solutions are expanded in a Fourier series with respect to the time variable $t$ and
the Chandrasekhar separation ansatz is applied so that the question of existence of a time-periodic solution is
reduced to the solvability of a certain coupled system of ordinary differential equations.
First, we prove the already known result that there are no time-periodic solutions in the non-extreme case.
Then it is shown that in the extreme case for fixed black hole data there is a sequence of particle masses
$(m_N)_{N\in\mathbb N}$ for which a time-periodic solution of the Dirac equation does exist.
The period of the solution depends only on the data of the black hole described by the Kerr-Newman metric.