Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity
International Journal of Applied Mathematics and Theoretical Physics
Volume 5, Issue 4, December 2019, Pages: 118-128
Received: Nov. 5, 2019;
Accepted: Nov. 28, 2019;
Published: Dec. 24, 2019
Views 415 Downloads 130
Siaka Massou, Department of Theoretical Physics and Mathematics, University of Abomey-Calavi, Abomey-Calavi, Benin
Alain Adomou, Department of Theoretical Physics and Mathematics, University of Abomey-Calavi, Abomey-Calavi, Benin; National Higher Institute of Industrial Technology, University of Abomey, Abomey, Benin
Jonas Edou, Department of Theoretical Physics and Mathematics, University of Abomey-Calavi, Abomey-Calavi, Benin
In this research work, we opt for the static spherical symmetric metric. Thus, taking into account the own gravitational field of elementary particles, we have obtained exact static spheric symmetric solutions of the nonlinear spinor and gravitational fields equations. The nonlinear terms in the spinor lagrangian density characterize the self-interaction of a spinor field. We have investigated in detail equations with power and polynomial nonlinearities. In this case, we have obtained exact regular solutions which have a localized energy density and limited total energy (soliton-like solutions) only if the mass parameter in the spinor field equations is equal to zero. In additional to this, the total charge and the total spin are bounded. We have also shown that in the linear case, soliton-like solutions are absent. But in the flat space-time, the obtained solutions are soliton-like configurations. Therefore, the proper gravitational field of elementary particles, the geometrical properties of the metric and the nonlinear terms in the lagrangian density play a crucial role in the purpose to get the regular solutions with localized energy density and limited total energy.
Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity, International Journal of Applied Mathematics and Theoretical Physics.
Vol. 5, No. 4,
2019, pp. 118-128.
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cadavid, A. C. and Finkelstein, R. J. (2001) J. Math. Physics, 42, 4419.
Poplawski, N. J. (2009) Modern Physics Letters, 24, 431442.
Ponomarev, V. N. and Obukhov, Yu. N., (1981) Gen.Relativ.Gavity, 13, 1037.
Rybakov, Yu. P., Shikin, G. N. and Saha, B., (1997) Int.Theor.Phys., 36, 1475.
Adomou, A. and Shikin, G. N. (1998) Izvestia VUZov, Fizika, 41, 69.
Adanhoum`e, A., Adomou, A., Codo, F.P. and Hounkonnou, M.N. (2012) Journal of Modern Physics, 3, 935 . https://doi.org/10.4236/jmp.2012.39122
saha, B. and Shikin, G. N. (2003) Czechoslovak Journal of Physics, 54, 597-620. https://doi.org/10.1023/B:CJOP.0000029690.61308.a5
Adomou, A., Edou, J. and Massou, S. (2019) Journal of Modern Physics, 10, 1222-1234. https://doi.org/10.4236/jmp.2019.1010081
Adomou, A., Edou, J. and Massou, S. (2019) Journal of Applied Mathematics and Physics, 7, 2018-2835. https://doi.org/10.4236/jamp.2019.711194
Shikin, G. N. (1995) Theory of Solitons in General Relativity. URSS, Moscow.
Heisenberg, W. , (1966) Introduction to Unified Field Theory of Elementary Particles. Interscience Publishers, London.
Adomou, A., Alvarado, R. and Shikin, G. N. (1995) Izvestiya Vuzov. Fizika, 863-868.
Zhelnorovich, V. A. (1982) spinor Theory and Its applications in Physics and Mechanics. Nauka, Moscow.
Bogoliliubov, N. N. and Shirkov, D. V. (1976) Introduction to the theory of Quantized Fields. Nauka, Moscow.
Rainer Burghardt (2019) Journal of Modern Physics, 10, 1439-1453 . https://doi.org/10.4236/jmp.2019.1012096
Slobodan Spremo (2019) Journal of Modern Physics, 10, 1532-1547 . https://doi.org/10.4236/jmp.2019.1013102
Petkov, V. (2010) Minkowski spacetime: A Hundred Years Later, New York . https://doi.org/10.1007/978-90-481-3475-5