 06167 Monika Winklmeier, Osanobu Yamada
 Spectral Analysis of Radial Dirac Operators in the KerrNewman Metric and its Applications to Timeperiodic Solutions
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May 30, 06

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Abstract. We investigate the existence of timeperiodic solutions of the Dirac equation in the KerrNewman 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 timeperiodic 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 timeperiodic solutions in the nonextreme 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 timeperiodic solution of the Dirac equation does exist.
The period of the solution depends only on the data of the black hole described by the KerrNewman metric.
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