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Spectral Analysis of Radial Dirac Operators in the Kerr-Newman Metric and its Applications to Time-periodic Solutions

Monika Winklmeier·Osanobu Yamada
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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.

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Monika Winklmeier, Osanobu Yamada. 2006-10-27. Spectral Analysis of Radial Dirac Operators in the Kerr-Newman Metric and its Applications to Time-periodic Solutions. https://doi.org/10.1063/1.2358394

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