Abstract
The self-conjugate Dirac Hamiltonian is obtained in the Kerr–Newman field. A transition is implemented to a Schrödinger-type relativistic equation. For the case where the angular and radial variables are not separated, the method of obtaining effective potentials is generalized. Effective potentials have isolated singularities on the event horizons as well as at certain parameters of the Kerr–Newman field and of the fermion in the neighborhoods of some values of the radial coordinate. For the extreme Kerr–Newman field, the impossibility of existence of stationary bound states of half-spin particles is proved.
Similar content being viewed by others
References
E. Schrödinger, I. Sitzber. Preuss. Akad. Wiss. 11–12, 105 (1932).
G. C. McVittie, Mon. Not. Roy. Astron. Soc. 92, 868 (1932).
D. R. Brill and J. M. Cohen, J. Math. Phys. 7, 238 (1966).
S. Chandrasekhar, Proc. Roy. Soc. London A 349, 571 (1976).
S. Chandrasekhar, Proc. Roy. Soc. London A 350, 565 (1976).
D. Page, Phys. Rev. D 14, 1509 (1976).
F. Belgiorno, Phys. Rev. D 58, 084017 (1998).
J. M. Cohen and R. T. Powers, Comm. Math. Phys. 86, 69 (1982).
A. Zecca, Nuovo Cim. B 113, 1309 (1998).
F. Belgiorno and M. Martellini, Phys. Lett. B 453, 17 (1999).
F. Belgiorno and S. L. Cacciatori, J. Math. Phys. 51, 033517 (2010).
M. Winklmeier and O. Yamada, J. Phys.A 42, 295204 (15) (2009).
M. Winklmeier and O. Yamada, J. Math. Phys. 47, 102503 (2006).
D. Batic, H. Schmid, and M. Winklmeier, J. Math. Phys. 46, 012504 (2005).
F. Finster, N. Kamran, J. Smoller, and S.-T. Yau, Comm. Pure Appl.Math. 53, 902 (2000).
F. Finster, N. Kamran, J. Smoller, and S.-T. Yau, Comm. Pure Appl.Math. 53, 1201 (2000).
F. Finster, N. Kamran, J. Smoller, and S.-T. Yau, Comm. Math. Phys. 230, 201 (2002).
F. Finster, N. Kamran, J. Smoller, and S.-T. Yau, Adv. Theor. Math. Phys. 7, 25 (2003).
F. Melnyk, Class. Quantum Grav. 17, 2281 (2000).
A. Caceres and C. Doran, Phys. Rev. A 72, 022103 (2005).
M. V. Gorbatenko and V. P. Neznamov. Phys. Rev. D 82, 104056 (2010).
M. V. Gorbatenko and V. P. Neznamov. Phys. Rev. D 83, 105002 (2011).
M. V. Gorbatenko and V. P. Neznamov. J.Mod. Phys. 6, 303 (2015).
M. V. Gorbatenko and V. P. Neznamov. Ann. Phys. (Berlin) 526, 491 (2014).
V. P. Neznamov and I. I. Safronov, Int. J. Mod. Phys. D 25, 1650091 (2016); arXiv: 1605/07450.
D. Batic and H. Schmid, Prog. Theor. Phys. 116, 517 (2006).
D. Batic and H. Schmid, Revista Colomb. Mat. 42, 183 (2008).
K. G. Suffern, E. D. Fackerell, and C.M. Cosgrove, J. Math. Phys. 24, 1350 (1983).
A. S. Tahvildar-Zadeh, J. Math. Phys. 56, 042501 (2015).
M. K.-H. Kiessling and A. S. Tahvildar-Zadeh, J. Math. Phys. 56, 042303 (2015).
K. M. Case, Phys. Rev. 80, 797 (1950).
Ya. B. Zeldovich and V. S. Popov, Uspekhi Fiz. Nauk 105, issue 3 (1971).
V. P. Neznamov. VANT, ser. Theoretical and applied physics, issue 1, p. 33 (2016).
M. V. Gorbatenko, V. P. Neznamov, and E. Yu. Popov, J. Physi. Conf. Series 678, 012037 (2016); arXiv: 1511.05058.
M. V. Gorbatenko, V. P. Neznamov, E. Yu. Popov, and I. I. Safronov, J. Phys. Conf. Series 678, 012036 (2016); arXiv: 1511.05482. DOI:10.1088/1742-6596/678/1/012036
V. P. Neznamov and V. E. Shemarulin, VANT, ser. Theoretical and applied physics, issue 3, p. 3 (2016).
V. P. Neznamov and V. E. Shemarulin, Grav. Cosmol. 23 149 (2017).
H. Quevedo, Int. J. Mod. Phys. D 20, 1779 (2011).
C. M. Bender, D. Brody, and H. F. Jones, Phys. Rev. Lett. 89, 2704041 (2002)
C. M. Bender, D. Brody, and H. F. Jones, Phys. Rev. D 70, 025001 (2004).
A. Mostafazadeh, J. Math Phys. 43, 205 (2002)
A. Mostafazadeh, J. Math Phys. 43, 2814 (2002)
A. Mostafazadeh, J. Math Phys. 43, 3944 (2002); arXiv: 0810.5643.
B. Bagchi and A. Fring, Phys. Lett. A 373, 4307 (2009); arXiv: 0907.5354.
M. V. Gorbatenko and V. P. Neznamov, Ann. Phys. (Berlin) 526, 195 (2014).
L. Parker, Phys. Rev. D 22, 1922 (1980).
A. Lasenby, C. Doran, J. Pritchard, A. Caceres, and S. Dolan, Phys. Rev. D 72, 105014 (2005).
D. R. Brill and J. A. Wheeler, Rev.Mod. Phys. 29, 465 (1957).
L. L. Foldy and S. A. Wouthuysen, Phys. Rev. 78, 29 (1950)
E. Eriksen, Phys. Rev. 111, 1011 (1958)
V. P. Neznamov, Part. Nucl. 37, 86 (2006)
V. P. Neznamov and A. J. Silenko, J. Math. Phys. 50, 122302 (2009)
A. J. Silenko, Theor. Math. Phys. 176, 987 (2013)
A. J. Silenko, Phys. Rev. A 91, 022103 (2015)
A. J. Silenko, Phys. Rev. A 93, 022108 (2016)
A. J. Silenko, Phys. Rev. A 94, 032104 (2016).
J. Dittrich and P. Exner, J. Math. Phys 26, 2000 (1985).
R. Penrose, Rivista del Nuovo Cimento, Serie I, 1, Numero Speciale: 252 (1969).
G. T. Horowitz and D. Marolf, Phys. Rev. D 52, 5670 (1995).
H. Schmid. Math. Nachrichten, 274–275, 117 (2004); math-ph/0207039.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Neznamov, V.P., Shemarulin, V.E. Analysis of Half-Spin Particle Motion in Kerr–Newman Field by Means of Effective Potentials in Second-Order Equations. Gravit. Cosmol. 24, 129–138 (2018). https://doi.org/10.1134/S0202289318020111
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0202289318020111