Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

Effect of f(R)-Gravity Models on Compact Stars

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We study the possibility of forming anisotropic compact stars in the framework of f(R)-modified gravity in a static spherically symmetric space-time. We find the unknown coefficients involved in the metric using masses and radii of the compact stars 4U 1820-30, Cen X-3, EXO 1785-248, and LMC X-4. We obtain the hydrostatic equilibrium equation for different forces and use the generalized Tolman-Oppenheimer-Volkoff equation to analyze the behavior of stars. Moreover, we verify the regularity conditions, anisotropic behavior, energy conditions, and stability of the compact stars. We use the effective energy-momentum tensor in f(R) gravity for the analysis. We show that in the framework of f(R) gravity theory, these compact stars have physically acceptable patterns. Our results here also agree with those in general relativity, which is a special case of f(R) gravity.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. Schwarzschild, “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie,” in: Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, Königlich Preussische Akademie der Wissenschaften, Berlin (1916), pp. 189–196; “On the gravitational field of a mass point according to Einstein’s theory,” Gen. Rel. Grav., 35, 951–959 (2003).

    Google Scholar 

  2. B. V. Ivanov, “Maximum bounds on the surface redshift of anisotropic stars,” Phys. Rev. D, 65, 104011 (2002); arXiv:gr-qc/0201090v2 (2002).

    Article  ADS  Google Scholar 

  3. S. K. Maurya and S. D. Maharaj, “Anisotropic fluid spheres of embedding class one using Karmarkar condition,” Eur. Phys. J. C, 77, 328 (2017); arXiv:1702.04192v1 [physics.gen-ph] (2017).

    Article  ADS  Google Scholar 

  4. R. L. Bowers and E. P. T. Liang, “Anisotropic spheres in general relativity,” Astrophys. J., 188, 657–665 (1974).

    Article  ADS  Google Scholar 

  5. R. Ruderman, “Pulsars: Structure and dynamics,” Ann. Rev. Astron. Astrophys., 10, 427–476 (1972).

    Article  ADS  Google Scholar 

  6. M. F. Shamir and M. Ahmad, “Some exact solutions in f(G, T) gravity via Noether symmetries,” Modern Phys. Lett. A, 32, 1750086.

  7. M. F. Shamir and M. Ahmad, “Noether symmetry approach in f(G, T) gravity,” Eur. Phys. J. C, 77, 55 (2017); arXiv:1611.07338v2 [physics.gen-ph] (2016).

    Article  ADS  Google Scholar 

  8. B. Li, T. P. Sotiriou, and J. B. Barrow, “f(T) gravity and local Lorentz invariance,” Phys. Rev. D, 83, 064035 (2011); arXiv:1010.1041v3 [gr-qc] (2010).

    Article  ADS  Google Scholar 

  9. T. Harko, F. S. N. Lobo, S. Nojiri, and S. D. Odintsov, “f(R, T) gravity,” Phys. Rev. D, 84, 024020 (2011); arXiv:1104.2669v2 [gr-qc] (2011).

    Article  ADS  Google Scholar 

  10. S. Capozziello, De M. Laurentis, S. D. Odintsov, and A. Stabile, “Hydrostatic equilibrium and stellar structure in f(R)-gravity,” Phys. Rev. D, 83, 064004 (2011); arXiv:1101.0219v1 [gr-qc] (2011).

    Article  ADS  Google Scholar 

  11. S. Nojiri and S. D. Odintsov, “unified cosmic history in modified gravity: From F(R) theory to Lorentz noninvariant models,” Phys. Rep., 505, 59–144 (2011); arXiv:1011.0544v4 [gr-qc] (2010).

    Article  ADS  MathSciNet  Google Scholar 

  12. S. Nojiri and S. D. Odintsov, “Modified f(R) gravity consistent with realistic cosmology: From a matter dominated epoch to a dark energy universe,” Phys. Rev. D, 74, 086005 (2006); arXiv:hep-th/0608008v3 (2006).

    Article  ADS  Google Scholar 

  13. D. Lovelock, “The Einstein tensor and its generalizations,” J. Math. Phys., 12, 498–501 (1971).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. T. Harko, “Evolution of cosmological perturbations in Bose-Einstein condensate dark matter,” Mon. Not. R. Astron. Soc., 413, 3095–3104 (2011); arXiv:1101.3655v2 [gr-qc] (2011).

    Article  ADS  Google Scholar 

  15. M. F. Shamir and T. Naz, “Compact stars with modified Gauss-Bonnet Tolman-Oppenheimer-Volkoff equation,” JETP, 128, 871–877 (2019).

    Article  ADS  Google Scholar 

  16. S. Nojiri, S. D. Odintsov, and V. K. Oikonomou, “Modified gravity theories on a nutshell: Inflation, bounce, and late-time evolution,” Phys. Rep., 692, 1–104 (2017); arXiv:1705.11098v2 [gr-qc] (2017).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. M. Sharif and A. Ikram, “Warm inflation in f(g) theory of gravity,” JETP, 123, 40–50 (2016).

    Article  ADS  Google Scholar 

  18. S. Capozziello, S. Nojiri, D. Odintsov, and A. Troisi, “Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase,” Phys. Lett. B, 639, 135–143 (2006); arXiv:astro-ph/0604431v3 (2006).

    Article  ADS  Google Scholar 

  19. L. Amendola, D. Polarski, and S. Tsujikawa, “Power-laws f(R) theories are cosmologically unacceptable,” Internat. J. Modern Phys. D, 16, 1555–1561 (2007); arXiv:astro-ph/0605384v2 (2006).

    Article  ADS  MATH  Google Scholar 

  20. L. Amendola, D. Polarski, and S. Tsujikawa, “Are f(R) dark energy models cosmologically viable?” Phys. Rev. Lett., 98, 131302 (2007).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. J. Santos and J. S. Alcaniz, “Energy conditions and Segre classification of phantom fields,” Phys. Lett. B, 619, 11–16 (2005).

    Article  ADS  Google Scholar 

  22. S. M. Carroll, M. Hoffman, and M. Trodden, “Can the dark energy equation-of-state parameter w be less than −1?” Phys. Rev. D, 68, 023509 (2003).

    Article  ADS  Google Scholar 

  23. J. S. Alcaniz, “Testing dark energy beyond the cosmological constant barrier,” Phys. Rev. D, 69, 083521 (2004); arXiv:astro-ph/0312424v2 (2003).

    Article  ADS  Google Scholar 

  24. J. D. Barrow and S. Hervik, “Anisotropically inflating universes,” Phys. Rev. D, 73, 023007 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  25. M. Visser, “Energy conditions in the epoch of galaxy formation,” Science, 276, 88–90 (1997); arXiv: 1501.01619v1 [gr-qc] (2015).

    Article  ADS  Google Scholar 

  26. J. Santos, J. S. Alcaniz, and M. J. Rebouças, “Energy conditions and supernovae observations,” Phys. Rev. D, 74, 067301 (2006).

    Article  ADS  Google Scholar 

  27. J. Santos, J. S. Alcaniz, M. J. Rebouças, and N. Pires, “Lookback time bounds from energy conditions,” Phys. Rev. D, 76, 043519 (2007); arXiv:0706.1779v2 [astro-ph] (2007).

    Article  ADS  Google Scholar 

  28. M. J. Rebouças and J. Santos, “Gödel-type universes in f(R) gravity,” Phys. Rev. D, 80, 063009 (2009).

    Article  ADS  Google Scholar 

  29. J. Santos, M. J. Rebouças, and T. B. R. F. Oliveira, “Godel-type universes in Palatini f(R)gravity,” Phys. Rev. D, 81, 123017 (2010); arXiv:1004.2501v2 [astro-ph.CO] (2010).

    Article  ADS  MathSciNet  Google Scholar 

  30. J. Wang, Y.-B. Wu, Y.-X. Guo, W.-Q. Yang, and L. Wang, “Energy conditions and stability in generalized f(R) gravity with arbitrary coupling between matter and geometry,” Phys. Lett. B, 689, 133–138 (2010); arXiv:1212.4921v1 [gr-qc] (2012).

    Article  ADS  MathSciNet  Google Scholar 

  31. K. Atazadeh, “Energy conditions in f(R) gravity and Brans-Dicke theories,” Internat. J. Modern Phys. D, 18, 1101–1111 (2009); arXiv:0811.4269v1 [gr-qc] (2008).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. A. Banijamali, B. Fazlpour, and M. R. Setare, “Energy conditions in f(G) modified gravity with non-minimal coupling to matter,” Astrophys. Space Sci., 338, 327–332 (2012).

    Article  ADS  MATH  Google Scholar 

  33. J. Wang and K. Liao, “Energy conditions in f(R, Lm) gravity,” Class. Q. Grav., 29, 215016 (2012).

    Article  ADS  MATH  Google Scholar 

  34. S. M. Hossein, F. Rahaman, J. Naskar, M. Kalam, and S. Ray, “Anisotropic compact stars with variable cosmological constant,” Internat. J. Modern Phys. D, 21, 1250088 (2012); arXiv:1204.3558v2 [gr-qc] (2012).

    Article  ADS  MATH  Google Scholar 

  35. B. V. Ivanov, “Analytical study of anisotropic compact star models,” Eur. Phys. J. C, 77, 738 (2017).

    Article  ADS  Google Scholar 

  36. D. Deb, S. R. Chowdhury, S. Ray, F. Rahaman, and B. K. Guha, “Relativistic model for anisotropic strange stars,” Ann. Phys., 387, 239–252 (2017); arXiv:1606.00713v2 [gr-qc] (2016).

    Article  ADS  MATH  Google Scholar 

  37. A. Aziz, S. Ray, and F. Rahaman, “A generalized model for compact stars,” Eur. Phys. J. C, 76, 248 (2016).

    Article  ADS  Google Scholar 

  38. A. V. Astashenok, S. Capozziello, and S. D. Odintsov, “Further stable neutron star models from f(R) gravity,” JCAP, 1312, 040 (2013); arXiv:1309.1978v2 [gr-qc] (2013).

    Article  ADS  Google Scholar 

  39. A. V. Astashenok and S. D. Odintsov, “From neutron stars to quark stars in mimetic gravity,” Phys. Rev. D, 94, 063008 (2016); arXiv:1512.07279v1 [gr-qc] (2015).

    Article  ADS  Google Scholar 

  40. A. V. Astashenok, S. Capozziello, and S. D. Odintsov, “Magnetic neutron stars in f(R) gravity,” Astrophys. Space Sci., 355, 333–341 (2015).

    Article  ADS  MATH  Google Scholar 

  41. M. Zubair and G. Abbas, “Study of anisotropic compact stars in Starobinsky model,” arXiv:1412.2120v3 [physics.gen-ph] (2014).

  42. A. V. Astashenok, S. D. Odintsov, and A. de la Cruz-Dombriz, “The realistic models of relativistic stars in f(R) = R + R2 gravity,” Class. Q. Grav., 34, 205008 (2017); arXiv:1704.08311v2 [gr-qc] (2017).

    Article  ADS  MATH  Google Scholar 

  43. A. V. Astashenok, S. Capozziello, and S. D. Odintsov, “Nonperturbative models of quark stars in f(R) gravity,” Phys. Lett. B, 742, 160–166 (2015); arXiv:1412.5453v2 [gr-qc] (2014).

    Article  ADS  MATH  Google Scholar 

  44. M. K. Jasim, “Anisotropic strange stars in Tolman-Kuchowicz spacetime,” Eur. Phys. J. C, 78, 603 (2018); arXiv:1801.10594v2 [gr-qc] (2018).

    Article  ADS  Google Scholar 

  45. R. C. Tolman, “Static solutions of Einstein’s field equations for spheres of fluid,” Phys. Rev., 55, 364–373 (1939).

    Article  ADS  MATH  Google Scholar 

  46. G. K. Patwardhan and P. C. Vaidya, “Relativistic distributions of matter of radial symmetry,” J. Univ. Bombay, n.s., 12, 23–36 (1943).

    MathSciNet  MATH  Google Scholar 

  47. A. L. Mehra, “Radially symmetric distribution of matter,” J. Austr. Math. Soc., 6, 153–155 (1966).

    Article  MATH  Google Scholar 

  48. B. Kuchowicz, “General relativistic fluid spheres: I. New solutions for spherically symmetric matter distributions,” Acta Phys. Pol., 33, 541–563 (1968).

    Google Scholar 

  49. C. Leibovitz, “Spherically symmetric static solutions of Einstein’s equations,” Phys. Rev. D, 185, 1664–1669 (1969).

    Article  ADS  MathSciNet  Google Scholar 

  50. S. K. Maurya, Y. K. Gupta, S. Ray, and B. Dayanandan, “Anisotropic models for compact stars,” Eur. Phys. J. C, 75, 225 (2015); arXiv:1504.00209v2 [gr-qc] (2015).

    Article  ADS  Google Scholar 

  51. A. A. Starobinsky, “A new type of isotropic cosmological models without singularity,” Phys. Lett. B, 91, 99–102 (1980).

    Article  ADS  MATH  Google Scholar 

  52. G. Cognola, “Class of viable modified f(R) gravities describing inflation and the onset of accelerated expansion,” Phys. Rev. D, 77, 046009 (2008).

    Article  ADS  Google Scholar 

  53. T. Clifton, “Further exact cosmological solutions to higher-order gravity theories,” Class. Q. Grav., 23, 7445–7454 (2006); arXiv:gr-qc/0607096v2 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  54. A. Ganguly, R. Gannouji, R. Goswami, and S. Ray, “Neutron stars in the Starobinsky model,” Phys. Rev. D, 89, 064019 (2014).

    Article  ADS  Google Scholar 

  55. A. Cooney, S. DeDeo, and D. Psaltis, “Neutron stars in f(R) gravity with perturbative constraints,” Phys. Rev. D, 82, 064033 (2010).

    Article  ADS  Google Scholar 

  56. D. Momeni and R. Myrzakulov, “Tolman-Oppenheimer-Volkoff equations in modified Gauss-Bonnet gravity,” Internat. J. Geom. Methods Modern Phys., 12, 1550014 (2015).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  57. H. Stephani, General Relativity, Cambridge Univ. Press, Cambridge (1990).

    MATH  Google Scholar 

  58. T. Güver, P. Wroblewski, L. Camarota, and F. Özel, “The mass and radius of the neutron star in 4U 1820–30,” Astrophys. J., 719, 1807–1812 (2010); arXiv:1002.3825v2 [astro-ph.HE] (2010).

    Article  ADS  Google Scholar 

  59. M. L. Rawls, J. A. Orosz, J. E. McClintock, M. A. P. Torres, C. D. Bailyn, and M. M. Buxton, “Refined neutron star mass determinations for six eclipsing X-ray pulsar binaries,” Astrophys. J., 730, 25 (2011).

    Article  ADS  Google Scholar 

  60. F. Özel, T. Güver, and T. Psaltis, “The mass and radius of the neutron star in EXO 1745–248,” Astrophys. J., 693, 1775–1789 (2009).

    Article  ADS  Google Scholar 

  61. Z. Yousaf, “Stellar filaments with Minkowskian core in the Einstein-A gravity,” Eur. Phys. J. Plus, 132, 276 (2017).

    Article  Google Scholar 

  62. K. Bamba, M. Ilyas, M. Z. Bhatti, and Z. Yousaf, “Energy conditions in modified f(G) gravity,” Gen. Rel. Grav., 49, 112 (2017).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  63. L. Herrera, “Cracking of self-gravitating compact objects,” Phys. Lett. A, 165, 206–210 (1992).

    Article  ADS  Google Scholar 

  64. H. Abreu, H. Hernández, and L. A. Núñez, “Sound speeds, cracking and the stability of self-gravitating anisotropic compact objects,” Class. Q. Grav., 24, 4631–4645 (2007).

    Article  ADS  MATH  Google Scholar 

Download references

Acknowledgments

The authors are very grateful to the anonymous reviewers for the valuable comments and suggestions for improving the paper.

Author information

Authors and Affiliations

  1. Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, Pakistan

    M. F. Shamir & I. Fayyaz

Authors
  1. M. F. Shamir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Fayyaz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to M. F. Shamir or I. Fayyaz.

Ethics declarations

Conflicts of interest. The authors declare no conflicts of interest.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 202, No. 1, pp. 126–142, January, 2020.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shamir, M.F., Fayyaz, I. Effect of f(R)-Gravity Models on Compact Stars. Theor Math Phys 202, 112–125 (2020). https://doi.org/10.1134/S0040577920010109

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040577920010109

Keywords

Search

Navigation