Teleparallel Killing Vectors of Non-Static Spherically Symmetric Space-Times

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-7
Year of Publication : 2021
Authors : Mushtaq Ahmed, Muhammad Ilyas
  10.14445/22315373/IJMTT-V67I7P517

MLA

MLA Style: Mushtaq Ahmed, Muhammad Ilyas  "Teleparallel Killing Vectors of Non-Static Spherically Symmetric Space-Times" International Journal of Mathematics Trends and Technology 67.7 (2021):141-149. 

APA Style: Mushtaq Ahmed, Muhammad Ilyas(2021). Teleparallel Killing Vectors of Non-Static Spherically Symmetric Space-Times International Journal of Mathematics Trends and Technology, 141-149.

Abstract
Killing symmetry equations in both cooridinate formalism and tetrad formalism form a system of coupled partial differential equations and require decoupling before integration. This discourse discovers the method of minimum partial differentiation and applies it to decouple teleparallel Killing equations for a non-static spherically symmetric space-time involving functions R(t) and λ(r). This method together with the method of separation of variables helps to decouple the basic system of teleparallel Killing equations and integrate. It finds that the function R(t) remains arbitrary for teleparallel Killing vectors where as for the function λ(r) there arise two cases. For one case the function λ(r) = - 1n r and for other it is not. It shows eight teleparallel Killing vector fields for the first case and seven teleparallel Killing vector fields for the second.

Reference

[1] Stephani H., General Relativity, Cambridge University Press, (1996), 2ed.
[2] Alexey Golovnev, Introduction to teleparallel gravities, arXiv: 1801.06929v1 (2018).
[3] Feroz, T., Mahmood, F. M., Qadir, A.: Nonlinear Dynamics, 45 (65)(2006).
[4] V. C. de Andrade and J. G. Pereira, Gravitational Lorentz force and the description of the gravitational interaction, Phys. Rev. D56, 4689 (1997).
[5] M. Schweizer and N. Straumann, Poincare gauge theory of gravitation and binary pulsar 1913+16, Phys. Lett. A71, 493 (1979).
[6] M. Schweizer and N. Straumann, and A. Wipf, Gen. Rel. Grav., 12, 951(1980).
[7] J. Nitsch and F. W. Hehl, Translational gauge theory of gravity: Post-Newtonian approximation and spin precession, Phys. Lett. B90, 98 (1980).
[8] Stephani H., General Relativity, Cambridge University Press, (1996), 2ed, 196.
[9] Killing, W., Uber die Grundlagen der Geometric, J. reine und Angrew. Math., 109 (1892) 121.
[10] Muhammad Sharif and Mohammed Jamil Amir, Teleparallel Killing Vectors of the Einstein universe, Mod. Phys. Lett. A, 23(2008) 963.
[11] Deniel Zwillinger., Handbook of Differential Equations, Acedemic Press, Inc. (London ), (1989) 176.
[12] Stephani H., General Relativity, Cambridge University Press, (1996), 2ed, 197.
[13] Bukhari A. H. and Qadir A., J. Maths. Phys., 31(1990) 1463
[14] Azad H. and Ziad M., Spherical symmetric manifolds which admit five isometries, J. Maths. Phys., 36(4) (1995) 1908
[15] Qadir A. and Ziad M., J. Maths. Phys., 29(1988) 2473
[16] Ziad M., Spherically symmetric space-times, Ph. D. thesis, Quaid azam University, Islamabad, Pakistan, (1990).
[17] Qadir A., J. Maths. Phys., 33(1992) 2262
[18] Mushtaq Ahmed and Quamar Javaid, Recent Progress In Symmetry Study of Space-times Symp. Trend Physics, Proc. Pakistan Physical Society, 4(1992) 73
[19] Mushtaq Ahmed and Qamar Javaid, On Symmetries of Space-times, Proceeding of all Pakistan mathematical Conference, ed. Zia Sadiq and Ziaullah Randhava, Pakistan Mathematical Society, Faisalabad, Pakistan, 1 (1997) 105.
[20] Mushtaq Ahmed, On number of Killing vector fields for specific non-static spherically symmetric space-times, M. Phil. thesis, Department of Mathematics, University of Karachi, 1997.

Keywords : Torsion fields, Teleparallel Killing vector fields, Weitzenbock connection, Method of minimum partial differentiation