Spherically-symmetric non-linear sigma model: the exact solutions obtained with isometrical embedding method


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Abstract

The method to generate exact cosmological solutions in the frame of the sphericallysymmetric non-linear sigma model is offered in the present paper. This method is based on the isometrical embeddings of the target space (non-linear sigma-model fields chiral space) into space-time. Also the method of application to two- and three-component chiral spaces embedded into space-time was considered. The exact cosmological solutions were obtained in the frame of the several special cases of the two- and three-component spherical-symmetric non-linear sigma-model. The obtained cosmological solutions were also investigated.

About the authors

Sergey V Chervon

I. N. Ulyanovs Ulyanovsk State Pedagogical University

Email: chervon.sergey@gmail.com
(д.ф.-м.н., проф.), профессор, каф. физики; Ульяновский государственный педагогический университет им. И. Н. Ульянова; I. N. Ulyanovs Ulyanovsk State Pedagogical University

Yulia A Svistunova

I. N. Ulyanovs Ulyanovsk State Pedagogical University

Email: u.a.svistunova@gmail.com
научный сотрудник, каф. физики; Ульяновский государственный педагогический университет им. И. Н. Ульянова; I. N. Ulyanovs Ulyanovsk State Pedagogical University

References

  1. Иванов Г. Г. Симметрии, законы сохранения и точные решения в нелинейной сигма-модели // ТМФ, 1983. Т. 57, № 1. С. 45-54; англ. пер.: Ivanov G. G. Symmetries, conservation laws, and exact solutions in nonlinear sigma models // Theoret. and Math. Phys., 1983. Vol. 57, no. 1. Pp. 981-987.
  2. Иванов Г. Г. Полиномиальные законы сохранения и точные решения, связанные с изометрическими и гомотетическими симметриями, в нелинейной сигма-модели // ТМФ, 1985. Т. 62, № 1. С. 144-152; англ. пер.: Ivanov G. G. Polynomial conservation laws and exact solutions associated with isometric and homothetic symmetries in the nonlinear sigma model // Theoret. and Math. Phys., 1985. Vol. 62, no. 1. Pp. 95-101.
  3. Chervon S. V. Chiral non-linear sigma model in general relativity and cosmology / In: Lecture Notes in Theoretical and Mathematical Physics. Kazan: Kazan State University Press, 2006. Pp. 108-172.
  4. Chervon S., Dahia F., Romero C. Harmonic maps and isometric embeddings of the spacetime // Phys. Lett. A, 2004. Vol. 326, no. 3-4. Pp. 171-177, arXiv: gr-qc/0312022.
  5. Chervon S., Romero C. The embedding of the space time in a target space of sigma model // Gen. Relativ. Gravitation, 2004. Vol. 36, no. 7. Pp. 1555-1561.
  6. Червон С. В., Свистунова Ю. А. Генерирование точных решений в трехкомпонентной самогравитирующей кинетической нелинейной сигма-модели с использованием изометрических погружений // Изв. вуз. Поволжский регион. Физ.-мат. науки, 2008. № 2. С. 95-106. [Chervon S. V., Svistunova Yu. A. Generation of exact solutions in threecomponent self-gravitating kinetic non-linear sigma model with the use of isometric embeddings // Izv. Vuz. Povolzhskiy Region. Fiz.-Mat. Nauki., 2008. no. 2. Pp. 95-106].
  7. Червон С. В. Плоско-симметричные решения в рамках SO(4)-инвариантной самогравитирующей нелинейной сигма-модели // Изв. вуз. Физика, 1983. Т. 26, № 8. С. 89- 93. [Chervon S. V. Plane-symmetric solutions of SO(4)-invariant non-linear self-gravitating sigma model // Izv. Vuz. Fizika, 1983. Vol. 26, no. 8. Pp. 89-93].
  8. Червон С. В. Нелинейные поля в теории гравитации и космологии. Ульяновск: УлГУ - Средне-Волжский НЦ, 1997. 191 с. [Chervon S. V. Non-linear fields in the theory of gravity and cosmology. Ul'yanovsk: UlGU - Sredne-Volzhskiy NC, 1997. 191 pp.]
  9. Dahia F., Romero C. The embedding of the spacetime in five dimensions: an extension of Campbell-Magaard theorem // J. Math. Phys., 2002. Vol. 43, no. 11. Pp. 5804-5814.
  10. Anderson E., Lidsey J. Embeddings in non-vacuum spacetimes // Class. Quant. Grav., 2001. Vol. 18, no. 22. Pp. 4831-4844.
  11. Anderson E., Dahia F., Lidsey J., Romero C. Embeddings in spacetimes sourced by scalar fields // J. Math. Phys., 2003. Vol. 44, no. 11. Pp. 5108-5119.
  12. Campbell J. A course of differential geometry. Oxford: Claredon Press, 1926. 261 pp.
  13. Magaard L. Zur Einbettung Riemannscher R¨ume in Einstein-R¨ume und konformeuclia a dische R¨ume: PhD Thesis. Kiel, 1963. a
  14. Dahia F., Romero C. The embedding of the spacetime in five-dimensional spaces with arbitrary non-degenerate Ricci tensor // J. Math. Phys., 2002. Vol. 43, no. 6. Pp. 3097-3106.
  15. Tolman R. C. Relativity, thermodynamics, and cosmology. Oxford: Clarendon Press, 1934. 519 pp.; русск. пер.: Толмен Р. Относительность, термодинамика и космология. М.: Наука, 1974. 520 с.
  16. Chervon S. V. Cosmological models of global universe evolution and decomposition of perturbations // Int. J. Mod. Phys. A, 2002. Vol. 17, no. 29. Pp. 4451-4456.

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