Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields

Jonas Edou; Alain Adomou; Valerie Ida Senan Hontinfinde; Siaka Massou

doi:doi:10.11648/j.ijass.20200804.11

| Peer-Reviewed

Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields

Jonas Edou, Alain Adomou, Valerie Ida Senan Hontinfinde, Siaka Massou

Published in International Journal of Astrophysics and Space Science (Volume 8, Issue 4)

Received: 26 March 2020 Accepted: 20 August 2020 Published: 11 January 2021

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The present research work deals with an extension of a previous work [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. We have obtained exact kink-like static spherical symmetric solutions to the self-consistent system of spinor and gravitational fields equations. The Einstein’s field equation shave been solved by the Liouville method. The principal difference between kink soliton with antikink soliton has been established. The nonlinear terms in the lagrangian are arbitrary functions F(I_S) depending on the invariant I_S = S²= ()². It is shown that the initial set of the Einstein and spinor field equations have regular solutions with a localized energy density of the spinor field only if m = 0 (m is the mass parameter in the spinor field equations). Equations with polynomial nonlinearities are thoroughly scrutinized. Let us emphasize that the spinor field with polynomial nonlinearities has a regular solutions with localized, positive and alternating energy density and finite total energy. In addition, the total charge and the total spin are also finte. We have also obtained exact solutions to the linear spinor field equations. We remarked that in this case soliton-like solutions are absent. Furthermore, we note that the properties of regular localized solutions depend on the symmetry and the nonlinear terms in the lagrangian of the self-consistent system of gravitational and spinor fields.

Published in	International Journal of Astrophysics and Space Science (Volume 8, Issue 4)
DOI	10.11648/j.ijass.20200804.11
Page(s)	32-40
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), 2024. Published by Science Publishing Group

Keywords

Lagrangian, Metric, Soliton-Like Solution

References

[1]	Scott, A. C., Chu, F. Y. F., and McLaughlin, D. W. (1973). Proc. IEEE61, 1443.
[2]	Shikin, G. N. (1995) Theory of Solitons in General Relativity. URSS, Moscow.
[3]	B. Saha, gr-qc/9811044v1, (1998)
[4]	Saha (2000) Soliton of scalar field with induced nonlinearity and their stability. International Journal of Modern Physics A, 15, No. 10, 1481-1496.
[5]	Adomou, A., Alvarado, R. and Shikin, G. N. (1995), Nonlinear spinor field equations in gravitaional theory, Izvestiya Vuzov. Fizika, 863-868.
[6]	Adomou, A. and Shikin, G. N. (1998), Exact static plane symmetric solutions to the nonlinear spinor field equations in the gravitational theory, Izvestia VUZov, Fizika, 41, 69.
[7]	saha, B. and Shikin, G. N. (2003), plane symmetric solitons of spinor and scalar fields, 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), plane symmetric solutions to the nonlinear spinor field equations in general relativity theory Journal of Modern Physics, 10, 1222-1234. https://doi.org/10.4236/jmp.2019.1010081
[9]	Adanhoumè, A., Adomou, A., Codo, F. P. and Hounkonnou, M. N. (2012), Nonlinear spinor field equations in gravitaional theory: spherical symmetric soliton-like solutions, Journal of Modern Physics, 3, 935. https://doi.org/10.4236/jmp.2012.39122
[10]	Adomou, A., Edou, J. and Massou, S. (2019), Soliton- like spherical symmetric solutions of the nonlinear spinor field equations depending on the invariant IP in the general relativity Theory, Journal of Applied Mathematics and Physics, 7, 2818-2835.
[11]	Massou, S., Adomou, A. and Edou, J. (2019), Soliton-like spherical symmetric solutions of the nonlinear spinor field equations in general relativity International Journal of Applied Mathematics and Theoretical Physics. Vol.5, N0.4,2019,pp.118-128. doi:10.11648/j.ijamtp.20190504.14.
[12]	Adomou, A., Edou, J., Hontinfinde S. I. V. and Massou, S. (2020), Exact Soliton-Like Spherical Symmetric solutions of Heisenberg-Ivanenko Nonlinear Spinor Field Equation in Gravitational Theory, Journal of Applied Mathematics and Physics, 8, 1236-1254.
[13]	Adomou, A., Edou, J., Hontinfinde S. I. V. and Massou, S. (2020), SPHERICAL SYMMETRIC SOLITONS OF SPINOR FIELD IN GRAVITATIONAL THEORY, International Journal of Advanced Research, 8 (6), 1331- 1340.
[14]	Kulyabov D. S., Rybakov Yu. P., Shikin G. N., Yuschenko L. P., math-ph/9902011v1, (1999).
[15]	Katzin, G. H., Livine, J. and Davis, W. R. (1969) Curvature collineation: A fundamental symmetry property of the space-times of the general relativity defined by the vanishing Lie derivative of the Riemann curvature tensor. Journal of Mathematical Physics, 10, 617-620.
[16]	Katzin, G. H., Livine, J. and Davis, W. R. (1970) Groups of Curvature collineation in Riemannian space-times which admit fields of parallel vectors. Journal of Mathematical Physics, 11, 1578-1580.
[17]	Katzin, G. H. an d Livine, J. Applications of Lie derivatives to symmetries, geodesic mappings, and first integrals in Riemannian spaces. Collection of articles commemorating Wladyslaw Slebodzinski. Colloquium Mathematicum XXVI 26 (1972) 21, Tensor (N. S.), 22 (1971) 64.
[18]	Norris, L. K., Green, L. H. and Davis, W. R. Fluid space-times including electromagnetic fields admitting symmetry mappings belonging to the family of contracted Ricci collineations. Journal of Mathematical Physics. 18 (1977), no. 7, 13051311.
[19]	Zhelnorovich, V. A. (1982) Theory of spinors and its applications to Physics and Mechanics. Nauka, Moscow.
[20]	Bogoliubov, N. N. and Shirkov, D. V. (1976) Introduction to the theory of Quantized Fields. Nauka, Moscow.
[21]	D. Brill and J. Wheeler, Rev. Mod. Phys. 29, 465 (1957).
[22]	Heisenberg, W., (1966) Introduction to Unified Field Theory of Elementary Particles. Interscience Publishers, London.

Cite This Article

Plain Text BibTeX RIS

APA Style

Jonas Edou, Alain Adomou, Valerie Ida Senan Hontinfinde, Siaka Massou. (2021). Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. International Journal of Astrophysics and Space Science, 8(4), 32-40. https://doi.org/10.11648/j.ijass.20200804.11

Copy | Download

ACS Style

Jonas Edou; Alain Adomou; Valerie Ida Senan Hontinfinde; Siaka Massou. Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. Int. J. Astrophys. Space Sci. 2021, 8(4), 32-40. doi: 10.11648/j.ijass.20200804.11

Copy | Download

AMA Style

Jonas Edou, Alain Adomou, Valerie Ida Senan Hontinfinde, Siaka Massou. Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. Int J Astrophys Space Sci. 2021;8(4):32-40. doi: 10.11648/j.ijass.20200804.11

Copy | Download

@article{10.11648/j.ijass.20200804.11,
  author = {Jonas Edou and Alain Adomou and Valerie Ida Senan Hontinfinde and Siaka Massou},
  title = {Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields},
  journal = {International Journal of Astrophysics and Space Science},
  volume = {8},
  number = {4},
  pages = {32-40},
  doi = {10.11648/j.ijass.20200804.11},
  url = {https://doi.org/10.11648/j.ijass.20200804.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijass.20200804.11},
  abstract = {The present research work deals with an extension of a previous work [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. We have obtained exact kink-like static spherical symmetric solutions to the self-consistent system of spinor and gravitational fields equations. The Einstein’s field equation shave been solved by the Liouville method. The principal difference between kink soliton with antikink soliton has been established. The nonlinear terms in the lagrangian are arbitrary functions F(IS) depending on the invariant IS = S2= ()2. It is shown that the initial set of the Einstein and spinor field equations have regular solutions with a localized energy density of the spinor field only if m = 0 (m is the mass parameter in the spinor field equations). Equations with polynomial nonlinearities are thoroughly scrutinized. Let us emphasize that the spinor field with polynomial nonlinearities has a regular solutions with localized, positive and alternating energy density and finite total energy. In addition, the total charge and the total spin are also finte. We have also obtained exact solutions to the linear spinor field equations. We remarked that in this case soliton-like solutions are absent. Furthermore, we note that the properties of regular localized solutions depend on the symmetry and the nonlinear terms in the lagrangian of the self-consistent system of gravitational and spinor fields.},
 year = {2021}
}

Copy | Download

TY - JOUR
T1 - Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields
AU - Jonas Edou
AU - Alain Adomou
AU - Valerie Ida Senan Hontinfinde
AU - Siaka Massou
Y1 - 2021/01/11
PY - 2021
N1 - https://doi.org/10.11648/j.ijass.20200804.11
DO - 10.11648/j.ijass.20200804.11
T2 - International Journal of Astrophysics and Space Science
JF - International Journal of Astrophysics and Space Science
JO - International Journal of Astrophysics and Space Science
SP - 32
EP - 40
PB - Science Publishing Group
SN - 2376-7022
UR - https://doi.org/10.11648/j.ijass.20200804.11
AB - The present research work deals with an extension of a previous work [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. We have obtained exact kink-like static spherical symmetric solutions to the self-consistent system of spinor and gravitational fields equations. The Einstein’s field equation shave been solved by the Liouville method. The principal difference between kink soliton with antikink soliton has been established. The nonlinear terms in the lagrangian are arbitrary functions F(IS) depending on the invariant IS = S2= ()2. It is shown that the initial set of the Einstein and spinor field equations have regular solutions with a localized energy density of the spinor field only if m = 0 (m is the mass parameter in the spinor field equations). Equations with polynomial nonlinearities are thoroughly scrutinized. Let us emphasize that the spinor field with polynomial nonlinearities has a regular solutions with localized, positive and alternating energy density and finite total energy. In addition, the total charge and the total spin are also finte. We have also obtained exact solutions to the linear spinor field equations. We remarked that in this case soliton-like solutions are absent. Furthermore, we note that the properties of regular localized solutions depend on the symmetry and the nonlinear terms in the lagrangian of the self-consistent system of gravitational and spinor fields.
VL - 8
IS - 4
ER -

Copy | Download

Author Information

Jonas Edou

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
Valerie Ida Senan Hontinfinde

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

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Jonas Edou, Alain Adomou, Valerie Ida Senan Hontinfinde, Siaka Massou. (2021). Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. International Journal of Astrophysics and Space Science, 8(4), 32-40. https://doi.org/10.11648/j.ijass.20200804.11

Copy | Download

ACS Style

Jonas Edou; Alain Adomou; Valerie Ida Senan Hontinfinde; Siaka Massou. Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. Int. J. Astrophys. Space Sci. 2021, 8(4), 32-40. doi: 10.11648/j.ijass.20200804.11

Copy | Download

AMA Style

Jonas Edou, Alain Adomou, Valerie Ida Senan Hontinfinde, Siaka Massou. Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. Int J Astrophys Space Sci. 2021;8(4):32-40. doi: 10.11648/j.ijass.20200804.11

Copy | Download

@article{10.11648/j.ijass.20200804.11,
  author = {Jonas Edou and Alain Adomou and Valerie Ida Senan Hontinfinde and Siaka Massou},
  title = {Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields},
  journal = {International Journal of Astrophysics and Space Science},
  volume = {8},
  number = {4},
  pages = {32-40},
  doi = {10.11648/j.ijass.20200804.11},
  url = {https://doi.org/10.11648/j.ijass.20200804.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijass.20200804.11},
  abstract = {The present research work deals with an extension of a previous work [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. We have obtained exact kink-like static spherical symmetric solutions to the self-consistent system of spinor and gravitational fields equations. The Einstein’s field equation shave been solved by the Liouville method. The principal difference between kink soliton with antikink soliton has been established. The nonlinear terms in the lagrangian are arbitrary functions F(IS) depending on the invariant IS = S2= ()2. It is shown that the initial set of the Einstein and spinor field equations have regular solutions with a localized energy density of the spinor field only if m = 0 (m is the mass parameter in the spinor field equations). Equations with polynomial nonlinearities are thoroughly scrutinized. Let us emphasize that the spinor field with polynomial nonlinearities has a regular solutions with localized, positive and alternating energy density and finite total energy. In addition, the total charge and the total spin are also finte. We have also obtained exact solutions to the linear spinor field equations. We remarked that in this case soliton-like solutions are absent. Furthermore, we note that the properties of regular localized solutions depend on the symmetry and the nonlinear terms in the lagrangian of the self-consistent system of gravitational and spinor fields.},
 year = {2021}
}

Copy | Download