Skip to main content
SpringerLink
Log in

Evolution of expansion-free massive stellar object in f(R, T) gravity

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

This paper explores an expansion-free model of a cluster of stars in the f(R, T) gravity. We consider a dissipative anisotropic viscous model of the star cluster. The mathematical modeling of a cluster of stars involving field equations, junction condition and dynamical equations is presented. The circumferential and relative radial velocities of the evolving layers of fluids are used to describe the physical meaning of expansion and shear effects. It is concluded that the expansion-free evolution of the star cluster contains a vacuum cavity within it. The relative velocity between the neighboring layers of fluids determines the cluster’s expansion-free and shear-free collapse. The Skripkin model with constant density is equivalent to the non-dissipative expansion-free isotropic star cluster. For the shear-free scenario, this model demonstrates homologous evolution. Finally, it is found that the f(R, T) gravitational terms indicating dark matter’s contribution to a star cluster have a significant impact on the dynamics of expansion-free evolution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Data Availability

No data associated in the manuscript.

References

  1. A. Boyarsky et al., Phys. Rev. Lett. 113, 251301 (2014)

    Article  ADS  Google Scholar 

  2. S.M. Carroll et al., Phys. Rev. D 70, 043528 (2004)

    Article  ADS  Google Scholar 

  3. S. Capozziello, A. Stabile, A. Troisi, Class. Quantum Gravity 25, 085004 (2008)

    Article  ADS  Google Scholar 

  4. G.J. Olmo, Phys. Rev. D 75, 023511 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  5. W. Hu, I. Sawicki, Phys. Rev. D 76, 064004 (2007)

    Article  ADS  Google Scholar 

  6. C.S.J. Pun, Z. Kovacs, T. Harko, Phys. Rev. D 78, 024043 (2006)

    Article  ADS  Google Scholar 

  7. L. Amendola, S. Tsujikawa, Phys. Lett. B 660, 125 (2008)

    Article  ADS  Google Scholar 

  8. C.G. Bertolami et al., Phys. Rev. D 75, 104016 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  9. T. Harko, Phys. Lett. B 669, 376 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  10. S. Nojiri, S.D. Odintsov, Phys. Lett. B 599, 137 (2004)

    Article  ADS  Google Scholar 

  11. G. Allemandi et al., Phys. Rev. D 72, 063505 (2005)

    Article  ADS  Google Scholar 

  12. O. Bertolami, J. Paramos, Phys. Rev. D 77, 084018 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  13. V. Faraoni, Phys. Rev. D 76, 127501 (2007)

    Article  ADS  Google Scholar 

  14. T.P. Sotiriou, Phys. Lett. B 664, 225 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  15. O. Bertolami, J. Paramos, Class. Quantum Gravity 25, 245017 (2008)

    Article  ADS  Google Scholar 

  16. D. Puetzfeld, Y.N. Obukhov, Phys. Rev. D 78, 121501 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  17. V. Faraoni, Phys. Rev. D 80, 124040 (2009)

    Article  ADS  Google Scholar 

  18. T. Harko et al., Phys. Rev. D 84, 104022 (2013)

    Google Scholar 

  19. H. Shabani, M. Farhoudi, Phys. Rev. D 90, 044031 (2014)

    Article  ADS  Google Scholar 

  20. I. Ayuso, J.B. Jiménez, A. Cruz-Dombriz, Phys. Rev. D 91, 104003 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  21. M. Sharif, M. Zubair, J. Cosmol. Astropart. Phys. 2012, 028 (2012)

    Article  Google Scholar 

  22. M. Sharif, M. Zubair, Astrophys. Space Sci. 349, 457 (2014)

    Article  ADS  Google Scholar 

  23. I. Noureen et al., Eur. Phys. J C 75, 7 (2018)

    Google Scholar 

  24. M. Sharif, A. Waseem, Eur. Phys. J C 78, 10 (2018)

    Article  Google Scholar 

  25. Z. Yousaf et al., Eur. Phys. J C 78, 4 (2018)

    Article  Google Scholar 

  26. M. Ilyas et al., Astrophys. Space Sci 362, 1 (2017)

    Article  MathSciNet  Google Scholar 

  27. Zaregonbadi et al., Phys. Rev. D 94, 084052 (2016)

  28. Y.S. Myung, T. Moon, E.J. Son, Phys. Rev. D 83, 124009 (2011)

    Article  ADS  Google Scholar 

  29. J.R. Ipser, K.S. Thorne, Astrophys. J. 154, 251 (1968)

    Article  ADS  MathSciNet  Google Scholar 

  30. J.M.D. Kruijssen et al., MNRAS 414, 1364 (2011)

    Article  Google Scholar 

  31. R. Manzoor, W. Shahid, Phys. Dark Univ. 33, 100844 (2021)

    Article  Google Scholar 

  32. V.A. Skripkin, Doklady 135, 1183 (1960)

    MathSciNet  Google Scholar 

  33. L. Herrera, N.O. Santos, A. Wang, Phys. Rev. D 78, 084026 (2008)

    Article  ADS  Google Scholar 

  34. L. Herrera, G. Le Denmat, N.O. Santos, Phys. Rev. D 79, 087505 (2009)

    Article  ADS  Google Scholar 

  35. A. Di Prisco et al., Int. J. Mod. Phys. D 20, 2351 (2011)

    Article  ADS  Google Scholar 

  36. M. Sharif, Z. Yousaf, Can. J. Phys. 90, 865 (2012)

    Article  ADS  Google Scholar 

  37. L. Herrera, N.O. Santos, Phys. Rep. 286, 53 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  38. L. Herrera et al., Phys. Rev. D 69, 084026 (2004)

    Article  ADS  Google Scholar 

  39. L. Herrera, N.O. Santos, Phys. Rev. D 70, 084004 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  40. A.D. Prisco et al., Phys. Rev. D 76, 064017 (2007)

    Article  ADS  Google Scholar 

  41. L. Herrera et al., Phys. 18, 1 (2009)

    Google Scholar 

  42. S.D. Maharaj, Mon. Not. R. Astron. Soc. 375, 1265 (2007)

    Article  ADS  Google Scholar 

  43. M. Sharif, N. Bashir, Gen. Relativ. Gravit. 44, 1725 (2012)

    Article  ADS  Google Scholar 

  44. M. Sharif, M.Z. Bhatti, Gen. Relativ. Gravit. 44, 2811 (2012)

    Article  ADS  Google Scholar 

  45. V.A. Skripkin, Soviet Phys. Doklady 135, 1183 (1960)

  46. C. Misner, D. Sharp, Phys. Rev. 136, B571 (1964)

    Article  ADS  Google Scholar 

  47. M. Cahill, G. McVittie, J. Math. Phys. (N.Y.) 11, 1382 (1970)

    Article  ADS  Google Scholar 

  48. R. Chan, Mon. Not. R. Astron. Soc. 316, 588 (2000)

    Article  ADS  Google Scholar 

  49. H. Stephani et al., Exact Solutions to Einsteins Field Equations (Cambridge University Press, Cambridge, 2003)

    Book  Google Scholar 

  50. M. Demianski, Relativistic Astrophysics (Pergamon Press, Oxford, 1985)

    Google Scholar 

  51. R. Kippenhahn, A. Weigert, Stellar Structure and Evolution (Springer, Berlin, 1990)

    Book  MATH  Google Scholar 

  52. M. Schwarzschild, Structure and Evolution of the Stars (Dover, New York, 1958)

    Book  Google Scholar 

  53. L. Herrera, A. Di Prisco, Phys. Rev. D 55, 2044 (1997)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Management and Technology, Johar Town Campus, Lahore, 54782, Pakistan

    Rubab Manzoor & Kashif Ramzan

  2. Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, Pakistan

    M. Asim Farooq

Authors
  1. Rubab Manzoor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kashif Ramzan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Asim Farooq
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rubab Manzoor.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Manzoor, R., Ramzan, K. & Farooq, M.A. Evolution of expansion-free massive stellar object in f(R, T) gravity. Eur. Phys. J. Plus 138, 134 (2023). https://doi.org/10.1140/epjp/s13360-023-03734-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-023-03734-7

Search

Navigation