پیوندهای مفید
آمار
| تعداد نشریات | 8 |
| تعداد شماره‌ها | 417 |
| تعداد مقالات | 5,494 |
| تعداد مشاهده مقاله | 6,135,851 |
| تعداد دریافت فایل اصل مقاله | 5,380,595 |
Analysis of the vacuum solution of the five-dimensional Einstein field equations with negative cosmological constant via variational symmetries | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 2، دوره 6، شماره 2، خرداد 2025، صفحه 109-120 اصل مقاله (435.33 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2024.22702.1185 | ||
| نویسنده | ||
| Fatemeh Ahangari* | ||
| Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, P.O.Box 1993893973, Iran | ||
| چکیده | ||
| The Kaluza-Klein theory can be reckoned as a classical unified field theory of two of the significant forces of nature gravitation and electromagnetism. This formulation geometrically demonstrates the effects of a gravitational and an electromagnetic field by investigating a five-dimensional space with a metric con[1]structed via the spacetime metric and the four-potential of the electromagnetic field. For the purpose of exploring the influences of dimensionality on the distinct physical variables, inquiring into stationary Kaluza-Klein rotating fluids is of par[1]ticular significance. In this research, an extensive investigation of the variational symmetries for a specific vacuum solution of the (4+1)-dimensional Einstein field equations with negative cosmological constant is presented. For this purpose, first of all, the variational symmetries of our analyzed model are completely determined and the construction of the Lie algebra of the resulted symmetries is accurately analyzed. It is represented that the Lie algebra of local symmetries interrelated to the system of geodesic equations is non-solvable and not semi-simple and the algebraic organization of the derived quotient Lie algebra is accurately evaluated. Mainly, the adjoint representation group is effectively utilized intended for establishing an optimal system of group invariant solutions; which unequivocally yields a conjugate relation in the set of all one-dimensional symmetry subalgebras. Accordingly, the associated set of invariant solutions can be regarded as the slightest list from that the alternative invariant solutions of one-dimensional subalgebras are thoroughly determined unambiguously by virtue of transformations. Literally, all the corresponding local conservation laws of the resulted variational symmetries are totally calculated. Indeed, the symmetries of the metric of our analyzed space-time lead to the constants of motion for the point particles. | ||
| کلیدواژه‌ها | ||
| Variational symmetries؛ Einstein field equations؛ Kaluza-Klein theory؛ Adjoint representation؛ Conservation laws | ||
| مراجع | ||
|
[1] I. Barukci ˇ c´, N-th index D-dimensional Einstein gravitational field equations, BoD–Books on Demand, Norder[1]stedt, Germany, 2020.
[2] G. W. Bluman, A. F. Cheviakov, and S. C. Anco, Applications of symmetry methods to partial differential equations, vol. 168 of Applied Mathematical Sciences, Springer, New York, 2010.
[3] W. Davidson, A Petrov type I cylindrically symmetric solution for perfect fluid in steady rigid body rotation, Classical Quantum Gravity, 13 (1996), pp. 283–287.
[4] K. Godel ¨ , An example of a new type of cosmological solutions of Einstein’s field equations of gravitation, Rev. Modern Physics, 21 (1949), pp. 447–450.
[5] N. H. Ibragimov, Elementary Lie group analysis and ordinary differential equations, vol. 4 of Wiley Series in Mathematical Methods in Practice, John Wiley & Sons, Ltd., Chichester, 1999.
[6] A. H. Kara and F. M. Mahomed, A basis of conservation laws for partial differential equations, J. Nonlinear Math. Phys., 9 (2002), pp. 60–72. Special issue in honour of P. G. L. Leach on the occasion of his 60th birthday.
[7] A. Kushner, V. Lychagin, and V. Rubtsov, Contact Geometry and Nonlinear Differential Equations, Encyclopedia of Mathematics and its Applications, Cambridge University Press, 2006.
[8] P. J. Olver, Applications of Lie groups to differential equations, vol. 107 of Graduate Texts in Mathematics, Springer-Verlag, New York, 1986.
[9] L. V. Ovsiannikov, Group analysis of differential equations, Academic Press, Inc., New York-London, 1982. Translated from the Russian by Y. Chapovsky, Translation edited by William F. Ames.
[10] A. Prakash, Studies on gravitational field equations and important results of relativistic cosmology, Lulu Publication, NC, United States, 2019.
[11] R. Tikekar and L. K. Patel, Rotating cylindrically symmetric Kaluza-Klein fluid model, Pramana J. Phys., 55 (2000), pp. 361–368. | ||
|
آمار تعداد مشاهده مقاله: 303 تعداد دریافت فایل اصل مقاله: 132 |
||