Skip to main content
SpringerLink
Log in

Gravitational collapse of anisotropic compact stars in modified f(R) gravity

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

Abstract

The physically realistic model of compact stars undergoing gravitational collapse in f(R) gravity has been developed. We consider a more general model \( R + f(R) = R + k R^m \) and describe the interior space-time of gravitationally collapsing stars with separable form of metric admitting homothetic killing vector. We then investigate the junction conditions to match the interior space-time with exterior space-time. Considering all junction conditions, we find analytical solutions describing interior space-time metric, energy density, pressures and heat flux density of the compact stars undergoing gravitational collapse. We impose the energy conditions to the model for describing the realistic collapse of physically possible matter distribution for particular models of GR, \( R+k R^2 \) and \( R+k R^4 \) gravity. The comprehensive graphical analysis of all energy conditions shows that the model is physically acceptable and realistic. We additionally investigate the physical properties of collapsing stars which are useful to decipher the inherent nature of such gravitationally collapsing stars.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. A. Kenath, S.B. Gudennavar, C. Sivaram, Dark matter, dark energy, and alternate models: a review. Adv. Space Res. 60(1), 166–186 (2017)

    Article  ADS  Google Scholar 

  2. M. Sami. Dark Energy and Possible Alternatives (2009)

  3. M. Sami. A Primer on Problems and Prospects of Dark Energy (2009)

  4. J. Edmund, M. Copeland, S.T. Sami, Dynamics of dark energy. Int. J. Mod. Phys. D 15(11), 1753–1935 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  5. K. Garrett, G. Dūda, Dark Matter: A Primer. Advances in Astronomy 2011, 968283 (2011)

  6. S. Nojiri, S.D. Odintsov, Modified gravity with negative and positive powers of the curvature: Unification of the inflation and of the cosmic acceleration. Phys. Rev. D 68, 123512 (2003)

  7. S. Nojiri, S.D. Odintsov, Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models. Phys. Rept. 505, 59–144 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  8. S. Nojiri, S.D. Odintsov, V.K. Oikonomou, Modified gravity theories on a Nutshell: inflation, bounce and late-time evolution. Phys. Rept. 692, 1–104 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  9. S. Nojiri, S.D. Odintsov, Accelerating cosmology in modified gravity: from convenient f(r) or string-inspired theory to bimetric f(r) gravity. Int. J. Geomet. Methods Mod. Phys. 11(02), 1460006 (2014)

    Article  MathSciNet  Google Scholar 

  10. L. Sebastiani, R. Myrzakulov, F(r)-gravity and inflation. Int. J. Geomet. Methods Mod. Phys. 12(09), 1530003 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  11. J.R.L. Santos, P.H.R.S. Moraes, Cosmology from a running vacuum model driven by a scalar field. Int. J. Geomet. Methods Mod. Phys. 17(01), 2050016 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  12. S. Capozziello, M. De Laurentis, Extended theories of gravity. Phys. Rep. 509(4–5), 167–321 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  13. R. Durrer, R. Maartens, Dark Energy and Modified Gravity (2008)

  14. T.P. Sotiriou, V. Faraoni, \(f(r)\) theories of gravity. Rev. Mod. Phys. 82, 451–497 (2010)

    Article  ADS  Google Scholar 

  15. T. Kobayashi, K. Maeda, Relativistic stars in \(f(r)\) gravity, and absence thereof. Phys. Rev. D 78, 064019 (2008)

  16. T. Clifton, P.G. Ferreira, A. Padilla, C. Skordis, Modified gravity and cosmology. Phys. Rep. 513(1–3), 1–189 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  17. S. Capozziello, M. De Laurentis, S.D. Odintsov, A. Stabile, Hydrostatic equilibrium and stellar structure in \(f(r)\) gravity. Phys. Rev. D 83, 064004 (2011)

  18. S. Capozziello, M. De Laurentis, I. De Martino, M. Formisano, S.D. Odintsov, Jeans analysis of self-gravitating systems in \(f(r)\) gravity. Phys. Rev. D 85, 044022 (2012)

  19. E.V. Arbuzova, A.D. Dolgov, Explosive phenomena in modified gravity. Phys. Lett. B 700(5), 289–293 (2011)

    Article  ADS  Google Scholar 

  20. M. Sharif, Gravitational perfect fluid collapse in f(r) gravity. Astrophys. Space Sci. 331(1), 281–288 (2010)

    Article  ADS  Google Scholar 

  21. G. Abbas, M.S. Khan, Z. Ahmad, M. Zubair, Higher-dimensional inhomogeneous perfect fluid collapse in \(f(R)\) gravity. Eur. Phys. J. C 77(7), 443 (2017)

    Article  ADS  Google Scholar 

  22. H. Kausar, I. Noureen, Dissipative spherical collapse of charged anisotropic fluid in f(r) gravity. Eur. Phys. J. C 74, 2760 (2014)

    Article  ADS  Google Scholar 

  23. A. Borisov, B. Jain, P. Zhang, Spherical collapse in \(f(r)\) gravity. Phys. Rev. D 85, 063518 (2012)

  24. S. Capozziello, M. De Laurentis, R. Farinelli, S.D. Odintsov, Mass-radius relation for neutron stars in \(f(r)\) gravity. Phys. Rev. D 93, 023501 (2016)

  25. A.V. Astashenok, S. Capozziello, S.D. Odintsov, Further stable neutron star models from \(f(r)\) gravity. J. Cosmol. Astropart. Phys. 12, 040 (2013)

    Article  ADS  Google Scholar 

  26. A.V. Astashenok, S. Capozziello, S.D. Odintsov, Extreme neutron stars from extended theories of gravity. J. Cosmol. Astropart. Phys. 2015(01), 001 (2015)

    Article  MathSciNet  Google Scholar 

  27. A.V. Astashenok, S. Capozziello, S.D. Odintsov, V.K. Oikonomou, Extended gravity description for the gw190814 supermassive neutron star. Phys. Lett. B 811, 135910 (2020)

  28. A.V. Astashenok, S. Capozziello, S.D. Odintsov, V.K. Oikonomou, Causal limit of neutron star maximum mass in f(r) gravity in view of gw190814. Phys. Lett. B 816, 136222 (2021)

  29. A.V. Astashenok, S. Capozziello, S.D. Odintsov, V.K. Oikonomou, Novel stellar astrophysics from extended gravity. EPL (Europhys. Lett.) 134(5), 59001 (2021)

    Article  ADS  Google Scholar 

  30. S.D. Odintsov, V.K. Oikonomou, Neutron stars in scalar-tensor gravity with Higgs scalar potential. arXiv e-prints, arXiv:2104.01982 (2021)

  31. M. Kopp, S.A. Appleby, I. Achitouv, J. Weller, Spherical collapse and halo mass function in \(f(r)\) theories. Phys. Rev. D 88, 084015 (2013)

  32. J.-Q. Guo, D. Wang, A.V. Frolov, Spherical collapse in \(f(r)\) gravity and the belinskii-khalatnikov-lifshitz conjecture. Phys. Rev. D 90, 024017 (2014)

  33. R. Goswami, A.M. Nzioki, S.D. Maharaj, S.G. Ghosh, Collapsing spherical stars inf(r)gravity. Phys. Rev. D 90(8), 1 (2014)

    Article  Google Scholar 

  34. S. Chakrabarti, R. Goswami, S. Maharaj, N. Banerjee, Conformally flat collapsing stars in f(r) gravity. Gen. Rel. Gravit. 50(11), 1 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  35. M. Bhatti, Z. Yousaf, S. Hanif, Gravitational collapse in generalized teleparallel gravity. Eur. Phys. J. Plus 132(5), 1 (2017)

    Google Scholar 

  36. M. Sharif, G. Abbas, Dynamics of charged radiating collapse in modified Gauss–Bonnet gravity. Eur. Phys. J. Plus. 128, 102 (2013)

    Article  Google Scholar 

  37. G. Abbas, M. Tahir, Dynamics of the dissipative gravitational collapse in Einstein–Gauss–Bonnet gravity. Eur. Phys. J. Plus 133(11), 476 (2018)

    Article  Google Scholar 

  38. S. Guha, U. Ghosh, Dynamical conditions and causal transport of dissipative spherical collapse in f(r, t) gravity. Eur. Phys. J. Plus 136(4), 1 (2021)

    Article  Google Scholar 

  39. A.V. Astashenok, K. Mosani, S.D. Odintsov, G.C. Samanta, Gravitational collapse in general relativity and in r2-gravity: a comparative study. Int. J. Geomet. Methods Mod. Phys. 16(03), 1950035 (2019)

    Article  ADS  Google Scholar 

  40. V. Dzhunushaliev, V. Folomeev, On the linear stability of polytropic fluid spheres in r2 gravity. Int. J. Geomet. Methods Mod. Phys. 17(11), 2050165 (2020)

    Article  ADS  Google Scholar 

  41. M. Fathi, M. Mohseni, Gravitational collapse in repulsive \(r+\mu ^{4}/r\). Eur. Phys. J. Plus 131(10), 1 (2016)

  42. M. Sharif, Z. Yousaf, Charged adiabatic ltb gravitational collapse in f(r) gravity. Int. J. Theoret. Phys. 55(5), 1 (2015)

    MATH  Google Scholar 

  43. M. Sharif, A. Anwar, Higher-dimensional charged ltb collapse in f(r) gravity. Eur. Phys. J. Plus 133, 284 (2018)

    Article  Google Scholar 

  44. G. Pinheiro, R. Chan, Radiating gravitational collapse with shear viscosity revisited. Gen. Relativ. Gravit. 40(10), 2149–2175 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  45. S. Chowdhury, K. Pal, K. Pal, T. Sarkar, Collapse in f(r) gravity and the method of r matching. Eur. Phys. J. C 80(9), 1 (2020)

    Article  ADS  Google Scholar 

  46. N. Deruelle, M. Sasaki, Y. Sendouda, Junction conditions in f(R) theories of gravity. Progress Theoret. Phys. 119(2), 237–251 (2008)

    Article  ADS  Google Scholar 

  47. J.M.M. Senovilla, Junction conditions for \(f(r)\) gravity and their consequences. Phys. Rev. D 88, 064015 (2013)

    Article  ADS  Google Scholar 

  48. K. Mosani, G.C. Samanta, Dynamics of general barotropic stellar fluid in the framework of r + 2\(\alpha \)t gravity. Mod. Phys. Lett. A 35(12), 2050089 (2020)

Download references

Acknowledgements

The author is very grateful to Professor S. Odintsov for his comments and insightful suggestions throughout the research work.

Author information

Authors and Affiliations

  1. Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat, 395007, India

    Jay Solanki

Authors
  1. Jay Solanki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jay Solanki.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Solanki, J. Gravitational collapse of anisotropic compact stars in modified f(R) gravity. Eur. Phys. J. Plus 137, 557 (2022). https://doi.org/10.1140/epjp/s13360-022-02784-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-02784-7

Search

Navigation