Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity

Siaka Massou; Alain Adomou; Jonas Edou

doi:doi:10.11648/j.ijamtp.20190504.14

| Peer-Reviewed

Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity

Siaka Massou, Alain Adomou, Jonas Edou

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 5, Issue 4)

Received: 5 November 2019 Accepted: 28 November 2019 Published: 24 December 2019

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

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.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 5, Issue 4)
DOI	10.11648/j.ijamtp.20190504.14
Page(s)	118-128
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Lagrangian, Metric, Invariant, At Space-time

References

[1]	Cadavid, A. C. and Finkelstein, R. J. (2001) J. Math. Physics, 42, 4419.
[2]	Poplawski, N. J. (2009) Modern Physics Letters, 24, 431442.
[3]	Ponomarev, V. N. and Obukhov, Yu. N., (1981) Gen.Relativ.Gavity, 13, 1037.
[4]	Rybakov, Yu. P., Shikin, G. N. and Saha, B., (1997) Int.Theor.Phys., 36, 1475.
[5]	Adomou, A. and Shikin, G. N. (1998) Izvestia VUZov, Fizika, 41, 69.
[6]	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
[7]	saha, B. and Shikin, G. N. (2003) Czechoslovak Journal of Physics, 54, 597-620. https://doi.org/10.1023/B:CJOP.0000029690.61308.a5
[8]	Adomou, A., Edou, J. and Massou, S. (2019) Journal of Modern Physics, 10, 1222-1234. https://doi.org/10.4236/jmp.2019.1010081
[9]	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
[10]	Shikin, G. N. (1995) Theory of Solitons in General Relativity. URSS, Moscow.
[11]	Heisenberg, W. , (1966) Introduction to Unified Field Theory of Elementary Particles. Interscience Publishers, London.
[12]	Adomou, A., Alvarado, R. and Shikin, G. N. (1995) Izvestiya Vuzov. Fizika, 863-868.
[13]	Zhelnorovich, V. A. (1982) spinor Theory and Its applications in Physics and Mechanics. Nauka, Moscow.
[14]	Bogoliliubov, N. N. and Shirkov, D. V. (1976) Introduction to the theory of Quantized Fields. Nauka, Moscow.
[15]	Rainer Burghardt (2019) Journal of Modern Physics, 10, 1439-1453 . https://doi.org/10.4236/jmp.2019.1012096
[16]	Slobodan Spremo (2019) Journal of Modern Physics, 10, 1532-1547 . https://doi.org/10.4236/jmp.2019.1013102
[17]	Petkov, V. (2010) Minkowski spacetime: A Hundred Years Later, New York . https://doi.org/10.1007/978-90-481-3475-5

Cite This Article

Plain Text BibTeX RIS

APA Style

Siaka Massou, Alain Adomou, Jonas Edou. (2019). Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity. International Journal of Applied Mathematics and Theoretical Physics, 5(4), 118-128. https://doi.org/10.11648/j.ijamtp.20190504.14

Copy | Download

ACS Style

Siaka Massou; Alain Adomou; Jonas Edou. Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity. Int. J. Appl. Math. Theor. Phys. 2019, 5(4), 118-128. doi: 10.11648/j.ijamtp.20190504.14

Copy | Download

AMA Style

Siaka Massou, Alain Adomou, Jonas Edou. Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity. Int J Appl Math Theor Phys. 2019;5(4):118-128. doi: 10.11648/j.ijamtp.20190504.14

Copy | Download

@article{10.11648/j.ijamtp.20190504.14,
  author = {Siaka Massou and Alain Adomou and Jonas Edou},
  title = {Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {5},
  number = {4},
  pages = {118-128},
  doi = {10.11648/j.ijamtp.20190504.14},
  url = {https://doi.org/10.11648/j.ijamtp.20190504.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20190504.14},
  abstract = {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.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity
AU  - Siaka Massou
AU  - Alain Adomou
AU  - Jonas Edou
Y1  - 2019/12/24
PY  - 2019
N1  - https://doi.org/10.11648/j.ijamtp.20190504.14
DO  - 10.11648/j.ijamtp.20190504.14
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 118
EP  - 128
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20190504.14
AB  - 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.
VL  - 5
IS  - 4
ER  -

Copy | Download

Author Information

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
Jonas Edou

Department of Theoretical Physics and Mathematics, University of Abomey-Calavi, Abomey-Calavi, Benin

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Siaka Massou, Alain Adomou, Jonas Edou. (2019). Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity. International Journal of Applied Mathematics and Theoretical Physics, 5(4), 118-128. https://doi.org/10.11648/j.ijamtp.20190504.14

Copy | Download

ACS Style

Siaka Massou; Alain Adomou; Jonas Edou. Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity. Int. J. Appl. Math. Theor. Phys. 2019, 5(4), 118-128. doi: 10.11648/j.ijamtp.20190504.14

Copy | Download

AMA Style

Siaka Massou, Alain Adomou, Jonas Edou. Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity. Int J Appl Math Theor Phys. 2019;5(4):118-128. doi: 10.11648/j.ijamtp.20190504.14

Copy | Download

@article{10.11648/j.ijamtp.20190504.14,
  author = {Siaka Massou and Alain Adomou and Jonas Edou},
  title = {Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {5},
  number = {4},
  pages = {118-128},
  doi = {10.11648/j.ijamtp.20190504.14},
  url = {https://doi.org/10.11648/j.ijamtp.20190504.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20190504.14},
  abstract = {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.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field equations in General Relativity
AU  - Siaka Massou
AU  - Alain Adomou
AU  - Jonas Edou
Y1  - 2019/12/24
PY  - 2019
N1  - https://doi.org/10.11648/j.ijamtp.20190504.14
DO  - 10.11648/j.ijamtp.20190504.14
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 118
EP  - 128
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20190504.14
AB  - 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.
VL  - 5
IS  - 4
ER  -

Copy | Download