Nonexistence of time-periodic solutions of the Dirac equation in nonextreme Kerr-Newman-AdS spacetime
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2016
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| _version_ | 1866909315253665792 |
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| author | Wang, Yaohua Zhang, Xiao |
| author_facet | Wang, Yaohua Zhang, Xiao |
| contents | In non-extreme Kerr-Newman-AdS spacetime, we prove that there is no nontrivial Dirac particle which is $L^p$ for $0<p\leq\frac{4}{3}$ with arbitrary eigenvalue $λ$, and for $\frac{4}{3}<p\leq\frac{4}{3-2q}$, $0<q<\frac{3}{2}$ with eigenvalue $|λ|>q κ$, outside and away from the event horizon. By taking $q=\frac{1}{2}$, we show that there is no normalizable massive Dirac particle with mass greater than $\fracκ{2} $ outside and away from the event horizon in non-extreme Kerr-Newman-AdS spacetime, and they must either disappear into the black hole or escape to infinity, and this recovers the same result of Belgiorno and Cacciatori in the case of $Q=0$ obtained by using spectral methods. Furthermore, we prove that any Dirac particle with eigenvalue $|λ|<\fracκ{2}$ must be $L^2$ outside and away from the event horizon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1608_05249 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Nonexistence of time-periodic solutions of the Dirac equation in nonextreme Kerr-Newman-AdS spacetime Wang, Yaohua Zhang, Xiao General Relativity and Quantum Cosmology Classical Analysis and ODEs In non-extreme Kerr-Newman-AdS spacetime, we prove that there is no nontrivial Dirac particle which is $L^p$ for $0<p\leq\frac{4}{3}$ with arbitrary eigenvalue $λ$, and for $\frac{4}{3}<p\leq\frac{4}{3-2q}$, $0<q<\frac{3}{2}$ with eigenvalue $|λ|>q κ$, outside and away from the event horizon. By taking $q=\frac{1}{2}$, we show that there is no normalizable massive Dirac particle with mass greater than $\fracκ{2} $ outside and away from the event horizon in non-extreme Kerr-Newman-AdS spacetime, and they must either disappear into the black hole or escape to infinity, and this recovers the same result of Belgiorno and Cacciatori in the case of $Q=0$ obtained by using spectral methods. Furthermore, we prove that any Dirac particle with eigenvalue $|λ|<\fracκ{2}$ must be $L^2$ outside and away from the event horizon. |
| title | Nonexistence of time-periodic solutions of the Dirac equation in nonextreme Kerr-Newman-AdS spacetime |
| topic | General Relativity and Quantum Cosmology Classical Analysis and ODEs |
| url | https://arxiv.org/abs/1608.05249 |