Skip to main content
SpringerLink
Log in

A physically viable model for a compact star and its compactness bound

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

Abstract

In this paper, we generate exact solutions for anisotropic fluid spheres in the context of General Relativity. Some well-studied stellar solutions are shown to be subsets of the developed solution. Ours is a three-parameter (M, R, and A) family of solutions where M is the mass, R is the radius and the parameter A fixes the anisotropy. We demonstrate how the developed solutions can be utilized to model compact objects such as neutron and quark stars, particularly by considering the estimated masses and radii of PSR \(J0030+0451\), PSR \(J0348+0432\), PSR \(J0740+6620\) and SMC X \(-1\). We also obtain the maximum compactness bound for our class of stars which might be treated as an anisotropic generalization of the well-known Buchdahl compactness bound.

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
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Data availability

The data underlying this article are available in the public domain as cited in the references.

Code availability

Not applicable.

References

  1. J.H. Jeans, Mon. Not. R. Astron. Soc. 82, 122 (1922)

    Article  ADS  Google Scholar 

  2. A.G. Lemaitre, Gen. Relativ. Gravity 29, 641 (1997)

    Article  ADS  Google Scholar 

  3. A.G. Lemaitre, Ann. Soc. Sci. Brux. A53, 51 (1933)

    Google Scholar 

  4. R. Ruderman, Annu. Rev. Astron. Astrophys. 10, 427 (1972)

    Article  ADS  Google Scholar 

  5. V. Canuto, Ann. Rev. Astron. Astrophys. 12, 167 (1974)

    Article  ADS  Google Scholar 

  6. A.I. Sokolov, JEPT 79, 1137 (1980)

    Google Scholar 

  7. L. Herrera, L. Nez, Astrophys. J. 339, 339 (1989)

    Article  ADS  Google Scholar 

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

    Book  MATH  Google Scholar 

  9. F. Weber, Pulsars as Astrophysical Observations for Nuclear and Particle Physics (Institute of Physics, Bristol, 1990)

    Google Scholar 

  10. A.P. Martnez, H.P. Rojas, H.J.M. Cuesta, Eur. Phys. J. C. 29, 111 (2003)

    Article  ADS  Google Scholar 

  11. B.V. Ivanov, Int. J. Theor. Phys. 49, 1236 (2010)

    Article  Google Scholar 

  12. V.V. Usov, Phys. Rev. D 70, 067301 (2004)

    Article  ADS  Google Scholar 

  13. F.E. Schunck, E.W. Mielke, Class. Quantum Gravity 20, R301 (2003)

    Article  ADS  Google Scholar 

  14. R.L. Bowers, E.P.T. Liang, Astrophys. J. 188, 657 (1974)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  16. H. Bondi, Proc. R. Soc. Lond. A 281, 39 (1964)

    Article  ADS  Google Scholar 

  17. L. Herrera, G.J. Ruggeri, L. Witten, Astrophys. J. 234, 1094 (1979)

    Article  ADS  Google Scholar 

  18. L. Herrera, Phys. Rev. D 101, 104024 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  19. L. Herrera, N.O. Santos, Astropyhs. J. 438, 308 (1995)

    Article  ADS  Google Scholar 

  20. L. Herrera, J. Ospino, A. Di Prisco, Phys. Rev. D 77, 027502 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  21. S.K. Maurya, Y.K. Gupta, Astrophys. Space Sci. 344, 243 (2013)

    Article  ADS  Google Scholar 

  22. S.D. Maharaj, J.M. Sunzu, S. Ray, Eur. Phys. J. Plus 129, 3 (2014)

    Article  Google Scholar 

  23. M.K. Mak, T. Harko, Proc. R. Soc. Lond. 459, 393 (2003)

    Article  ADS  Google Scholar 

  24. T. Feroze, A.A. Siddiqui, Gen. Relativ. Gravity 43, 1025 (2011)

    Article  ADS  Google Scholar 

  25. S.D. Maharaj, P. Mafa Tasika, Gen Relativ Gravity 44, 1419 (2012)

    Article  ADS  Google Scholar 

  26. S.D. Maharaj, R. Maartens, Gen. Relativ. Graviity 21, 899 (1989)

    Article  ADS  Google Scholar 

  27. M. Cosenza, L. Herrera, M. Esculpi, L. Witten, J. Math. Phys. 22, 118 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  28. I. Lopes, G. Panotopoulos, Á. Rincón, Eur. Phys. J. Plus 134, 134–140 (2019)

    Article  Google Scholar 

  29. F. Tello-Ortiz, M. Malaver, A. Rincón, Y. Gomez-Leyton, Eur. Phys. J. C 80, 371 (2020)

    Article  ADS  Google Scholar 

  30. C. Arias, E. Contreras, E. Fuenmayor, A. Ramos, Ann. Phys. 436, 168671 (2022)

    Article  Google Scholar 

  31. A. Rincón, G. Panotopoulos, I. Lopes, Eur. Phys. J. C 83, 116 (2023)

    Article  ADS  Google Scholar 

  32. G. Panotopoulos, A. Rincón, Eur. Phys. J. Plus 134, 472 (2019)

    Article  Google Scholar 

  33. S.K. Maurya, A. Pradhan, F. Tello-Ortiz, A. Banerjee, R. Nag, Eur. Phys. J. C 81, 848 (2021)

    Article  ADS  Google Scholar 

  34. G. Panotopoulos, A. Rincón, I. Lopes, Eur. Phys. J. C 81, 63 (2021)

    Article  ADS  Google Scholar 

  35. S. Thirukkanesh, F.C. Ragel, R. Sharma, S. Das, Eur. Phys. J. C 78, 1 (2018)

    Article  ADS  Google Scholar 

  36. S. Thirukkanesh, R. Sharma, S.D. Maharaj, Eur. Phys. J. Plus 134, 378 (2019)

    Article  Google Scholar 

  37. K. Komathiraj, R. Sharma, Astrophys. Space Sci. 365, 181 (2020)

    Article  Google Scholar 

  38. K. Komathiraj, R. Sharma, S. Chanda, Astrophys. Space Sci. 367, 86 (2023)

    Article  ADS  Google Scholar 

  39. T. Harko, M.K. Mak, Chin. J. Astron. Astrophys. 2, 248 (2002)

    Article  ADS  Google Scholar 

  40. G. Panotopoulos, A. Rincón, Eur. Phys. J. C 79, 524 (2019)

    Article  ADS  Google Scholar 

  41. G. Panotopoulos, A. Rincón, I. Lopes, Eur. Phys. J. C 80, 318 (2020)

    Article  ADS  Google Scholar 

  42. G. Panotopoulos, I. Lopes, Phys. Rev. D 98, 083001 (2018)

    Article  ADS  Google Scholar 

  43. R. Sharma, S. Das, S. Thirukkanesh, Astrophys. Space Sci. 362, 232 (2017)

    Article  ADS  Google Scholar 

  44. A. Banerjee, T. Tangphati, S. Hansraj, A. Pradhan, Ann. Phys. 451, 169267 (2023)

    Article  Google Scholar 

  45. S. Das, R. Sharma, K. Chakraborty, L. Baskey, Gen. Relativ. Gravity 52, 101 (2020)

    Article  ADS  Google Scholar 

  46. B. Das, K.B. Goswami, P.K. Chattopadhyay, R. Sharma, Indian J. Phys. 97(8), 2273 (2023)

    Article  ADS  Google Scholar 

  47. B.C. Paul, S. Das, R. Sharma, Eur. Phys. J. Plus 137, 525 (2022)

    Article  Google Scholar 

  48. H.A. Buchdahl, Phys. Rev. 116, 1027 (1959)

    Article  ADS  MathSciNet  Google Scholar 

  49. R. Sharma, A. Ghosh, S. Bhattacharya, S. Das, Eur. Phys. J. C 81, 1 (2021)

    Article  ADS  Google Scholar 

  50. A. Giuliani, T. Rothman, Gen. Relativ. Gravity 40, 1427 (2008)

    Article  ADS  Google Scholar 

  51. R. Sharma, N. Dadhich, S. Das, S.D. Maharaj, Eur. Phys. J. C 81, 79 (2021)

    Article  ADS  Google Scholar 

  52. P.C. Vaidya, R. Tikekar, Astrophys. Astron. 3, 325 (1982)

    Article  ADS  Google Scholar 

  53. M.S.R. Delgaty, K. Lake, Comput. Phys. Commun. 115, 395 (1998)

    Article  ADS  Google Scholar 

  54. M. R. Finch ,J. E. F. Skea A Review of the Relativistic Static Fluid Sphere, unpublished, http://www.dft.if.uerj.br/users/JimSkea/papers/pfrev.ps (1998)

  55. L. Herrera, Phys. Lett. A 165, 206 (1992)

    Article  ADS  Google Scholar 

  56. H. Abreu, H. Hernandes, L.A. Nunenz, Class. Quantum Gravity 24, 4631 (2007)

    Article  ADS  Google Scholar 

  57. S.H. Hendi, G.H. Bordbar, B.E. Panah, S. Panahiyan, JCAP 9, 013 (2016)

    Article  ADS  Google Scholar 

  58. S.H. Hendi, G.H. Bordbar, B.E. Panah, S. Panahiyan, JCAP 7, 004 (2017)

    Article  ADS  Google Scholar 

  59. R. Chan, L. Herrera, N.O. Santos, Mon. Not. R. Astron. Soc. 265, 533 (1993)

    Article  ADS  Google Scholar 

  60. J. Ponce de Leon, Gen. Relativ. Gravity 25, 1123 (1993)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

RS gratefully acknowledge support from the Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, Govt. of India, under its Visiting Research Associateship Programme. We are also grateful to the anonymous referees for providing valuable suggestions.

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Department of Mathematics, Eastern University, Chenkalady, Sri Lanka

    S. Thirukkanesh

  2. Department of Physics, Cooch Behar Panchanan Barma University, Cooch Behar, West Bengal, 736101, India

    Arpita Ghosh & Ranjan Sharma

Authors
  1. S. Thirukkanesh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arpita Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ranjan Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All the authors have contributed equally.

Corresponding author

Correspondence to Ranjan Sharma.

Ethics declarations

Conflict of interest

The authors declare that they have no Conflict of interest.

Ethics approval

Yes.

Consent to participate

Yes.

Consent for publication

Yes.

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

Thirukkanesh, S., Ghosh, A. & Sharma, R. A physically viable model for a compact star and its compactness bound. Eur. Phys. J. Plus 138, 588 (2023). https://doi.org/10.1140/epjp/s13360-023-04216-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-023-04216-6

Search

Navigation