2006/05/31 by Monika Winklmeier, Osanobu Yamada · 3 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #gr-qc
paper · pdf · doi:10.1063/1.2358394
published as J.Math.Phys.47:102503,2006 · 15 pages
openalex publication_date 2006/10/01 · arxiv created 2006/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 nonextreme case. Then, it is shown that in the extreme case for fixed black hole data there is a sequence of particle masses (mN)N∊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.