Spectral analysis of radial Dirac operators in the Kerr-Newman metric and its applications to time-periodic solutions
May, 2006Citations per year
Abstract: (arXiv)
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 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 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.- 04.70.-s
- 02.30.Lt
- 97.60.Lf
- 02.30.Hq
- Dirac equation
- spectral analysis
- black holes
- Fourier series
- differential equations
- operator: Dirac
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