Stationary solutions of second-order equations for point fermions in the Schwarzschild gravitational field
| Autor: | Neznamov, V. P., Safronov, I. I. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | JETP Vol. 154 (4) 761-773 (2018); English transl. JETP Vol.127 (4) 647-658 (2018) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1134/S0044451018100073; |
| Popis: | When using a second-order Schr\"odinger-type equation with the effective potential of the Schwarzschild field, existence of a stationary state of half-spin particles with energy $E=0$ is proved. For each of the values of quantum numbers $j,l$, the physically meaningful energy $E=0$ (the binding energy is $E_{b}=mc^{2}$) is implemented at the value of the gravitational coupling constant $\alpha\geq\alpha_{min}$. The particles with $E=0$ are, with the overwhelming probability, at some distance from the event horizon within the range from zero to several fractions of Compton wavelength of a fermion depending on value of the gravitational coupling constants and values $j,l$. In this paper, similar solutions of the second-order equation are announced for bound states of fermions in the Reissner-Nordstr\"om, Kerr, Kerr-Newman fields. Atomic-type systems: collapsars with fermions in bound states are proposed as particles of dark matter. Comment: 23 pages, 2 figures, 1 table |
| Databáze: | arXiv |
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