New cylindrically symmetric solution of Einstein field equations their conservation laws and the particles dynamics

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

The study explores the particle dynamics, asymptotic behavior, and flatness in Riemann curvature corresponding to the solutions obtained from the Ricci tensor of cylindrical spacetimes. Since these solutions are non-Minkowskian and are proposed to have curvature in almost all the cases, that is why some cylindrically symmetric static vacuum solutions of Einstein Field Equations have been worked out. We explore the Noether symmetries along with their conservation laws of the corresponding static-spacetime and calculate the equation of motions by taking into account Noether symmetries. We study the dynamics of particle in the form of effective potential, effective force.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3

References

  1. [1]

    C W Misner, K S Thorne, J A Wheeler and W Gravitation Freeman and com- pany, San Francisco 891 (1973)

  2. [2]

    T Feroze, A Qadir and M Ziad J. Math. Phys. 42 4947 (2001)

    ADS  MathSciNet  Article  Google Scholar 

  3. [3]

    A Qadir and M Ziad Il Nuovo Cimento B 110 277 (1995)

    ADS  Article  Google Scholar 

  4. [4]

    F Ali and T Feroze Int. J. Theor. Phys. 52 3329 (2013)

    Article  Google Scholar 

  5. [5]

    I A Khan et al., Int. J. Mod. Phys. D. 29 2050095 (2020)

    ADS  Article  Google Scholar 

  6. [6]

    F Ali and T Feroze Mathematics 4 50 (2016)

    Article  Google Scholar 

  7. [7]

    B P Abbott et al., Phys. Rev. Lett. 119 161101 (2017)

    ADS  Article  Google Scholar 

  8. [8]

    F Acernese et al., Classical. Quant. Grav. 32 024001 (2014)

    ADS  Article  Google Scholar 

  9. [9]

    M Soares-Santos et al., Astrophys. J. Lett. 848 L16 (2017)

    ADS  Article  Google Scholar 

  10. [10]

    C M Will Living reviews in relativity 17 4 (2014)

  11. [11]

    M Isi and A J Weinstein arXiv preprintarXiv:1710.03794 (2017)

  12. [12]

    T Callister et al., Phys. Rev. X 7 041058 (2017)

    Google Scholar 

  13. [13]

    D N Spergel et al., Astrophys. J. Suppl 170 377 (2007)

  14. [14]

    Perlmutter et al., The Astrophys. J 517 565 (1999)

  15. [15]

    M Tegmark Phys. Rev. D. 69 103501 (2004)

  16. [16]

    U Seljak Phys. Rev. D. 71 103515 (2005)

  17. [17]

    M S Carroll Phys. Rev. Lett. 81 3067 (1998)

  18. [18]

    B Nayak and M Jamil Phys. Lett. B. 709 118 (2012)

    ADS  Article  Google Scholar 

  19. [19]

    C A Picon, V Mukhanov And J P Steinhard Phys. Rev. Lett. 85 4438 (2000)

    ADS  Article  Google Scholar 

  20. [20]

    D Kramer et al., Cambridge University Press(1980)

  21. [21]

    A S Khan and F Ali Phys. Dark. Universe. 100389 (2019)

  22. [22]

    G S Hall World Scientific, Singapore (2004)

  23. [23]

    P G Leach et al., J. Nonliear. Math. Phy. 8 139 (2001)

    ADS  Article  Google Scholar 

  24. [24]

    M Ali et al., Symmetry 11 4679 (2019)

    Google Scholar 

  25. [25]

    A S Khan et al., Mod. Phys. lett. A. 30 2050234 (2020)

    Article  Google Scholar 

  26. [26]

    T Callister et al., Phy. Rev. X. 7 041058 (2017)

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Israr Ali Khan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Khan, I.A., Khan, A.S., Ali, F. et al. New cylindrically symmetric solution of Einstein field equations their conservation laws and the particles dynamics. Indian J Phys (2021). https://doi.org/10.1007/s12648-021-02014-3

Download citation

Keywords

  • Einstein field equations
  • Ricci curvature tensors
  • Vacuum solutions
  • Black hole