Skip to main content
SpringerLink
Log in

A new exact anisotropic solution of embedding class one

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

Abstract.

We have presented a new anisotropic solution of Einstein’s field equations for compact-star models. Einstein’s field equations are solved by using the class-one condition (S.N. Pandey, S.P. Sharma, Gen. Relativ. Gravit. 14, 113 (1982)). We constructed the expression for the anisotropy factor (\( \Delta\) by using the pressure anisotropy condition and thereafter we obtained the physical parameters like energy density, radial and transverse pressure. These models parameters are well-behaved inside the star and satisfy all the required physical conditions. Also we observed the very interesting result that all physical parameters depend upon the anisotropy factor (\( \Delta\). The mass and radius of the present compact-star models are quite compatible with the observational astrophysical compact stellar objects like Her X-1, RXJ 1856-37, SAX J1808.4-3658(SS1), SAX J1808.4-3658(SS2).

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

Similar content being viewed by others

References

  1. M.G.B. de Avellar, J.E. Horvath, Int. J. Mod. Phys. D 19, 1937 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  5. F. Rahaman et al., Eur. Phys. J. C 74, 3126 (2014)

    Article  ADS  Google Scholar 

  6. M. Kalam et al., Eur. Phys. J. C 74, 2971 (2014)

    Article  ADS  Google Scholar 

  7. M. Kalam et al., Astrophys. Space Sci. 349, 865 (2014)

    Article  ADS  Google Scholar 

  8. M. Kalam et al., Int. J. Theor. Phys. 52, 3319 (2013)

    Article  MathSciNet  Google Scholar 

  9. M. Kalam et al., Eur. Phys. J. C 73, 2409 (2013)

    Article  ADS  Google Scholar 

  10. F. Rahaman et al., Astrophys. Space Sci. 330, 249 (2010)

    Article  ADS  Google Scholar 

  11. R. Ruderma, Rev. Astron. Astrophys. 10, 427 (1972)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. H. Abreu, H. Hernandez, L.A. Nunez, Class. Quantum. Grav. 24, 4631 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  14. S.K. Maurya, Y.K. Gupta, S. Ray, B. Dayanandan, Eur. Phys. J. C 75, 225 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. S.K. Maurya, Generalized relativistic anisotropic models for compact stars, arXiv:1511.01625 [gr-qc] (2015)

  17. S.K. Maurya, Y.K. Gupta, S. Ray, arXiv:1502.01915 [gr-qc] (2015)

  18. M. Chaisi, S.D. Maharaj, Pramana J. Phys. 66, 609 (2006)

    Article  ADS  Google Scholar 

  19. K. Komathiraj, S.D. Maharaj, J. Math. Phys. 48, 042501 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  20. S.D. Maharaj, R. Maartens, Gen. Relativ. Gravit. 21, 899 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  21. M. Esculpi, M. Malaver, E. Aloma, Gen. Relativ. Gravit. 39, 633 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  22. M.K. Mak, T. Harko, Proc. R. Soc. London, Ser. A 459, 393 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  23. K. Dev, M. Gleiser, Gen. Relativ. Gravit. 34, 1793 (2002)

    Article  MathSciNet  Google Scholar 

  24. P.H. Nguyen, M. Lingam, Mon. N. R. Astron. Soc. 436, 2014 (2013)

    Article  ADS  Google Scholar 

  25. M. Malaver, Am. J. Astron. Astrophys. 1, 41 (2013)

    Article  Google Scholar 

  26. U.S. Nilsson, C. Uggla, Ann. Phys. 286, 292 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  27. K. Dev, M. Gleiser, Gen. Relativ. Gravit. 35, 1435 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  28. M. Chaisi, S.D. Maharaj, Gen. Relativ. Gravit. 37, 1177 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  29. S.K. Maurya et al., Eur. Phys. J. C 76, 266 (2016)

    Article  ADS  Google Scholar 

  30. K. Schwarzschild, Sitzungsber. Dtsch. Akad. Wiss. Math.-Phys. Berlin 24, 424 (1916)

    Google Scholar 

  31. M. Kohler, K.L. Chao, Z. Naturforsch. Ser. A 20, 1537 (1965)

    ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  34. H. Abreu, H. Hernandez, L.A. Nunez, Class. Quantum Grav. 24, 4631 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  35. R.C. Tolman, Phys. Rev. 55, 364 (1939)

    Article  ADS  Google Scholar 

  36. J.R. Oppenheimer, G.M. Volkoff, Phys. Rev. 55, 374 (1939)

    Article  ADS  Google Scholar 

  37. D.D. Dionysiou, Astrophys. Space Sci. 85, 331 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  38. A.S. Eddington, The Mathematical Theory of Relativity (Cambridge University Press, Cambridge, 1924)

  39. A. Friedmann, Z. Phys. 10, 377 (1922)

    Article  ADS  Google Scholar 

  40. H.P. Robertson, Rev. Mod. Phys. 5, 62 (1933)

    Article  ADS  Google Scholar 

  41. G. Lemaitre, Ann. Soc. Sci. Bruxelles 53, 51 (1933)

    Google Scholar 

  42. R.R. Kuzeev, Gravit. Teor. Otnosct. 16, 93 (1980) (in Russian)

    MathSciNet  Google Scholar 

  43. J. Rayski, Preprint, Dublin Institute for Advance Studies (1976)

  44. M. Pavsic, V. Tapia, arXiv:gr-qc/0010045 (2001)

  45. K.R. Karmarkar, Proc. Ind. Acad. Sci. A 27, 56 (1948)

    MathSciNet  Google Scholar 

  46. S.N. Pandey, S.P. Sharma, Gen. Relativ. Gravit. 14, 113 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  47. V. Canuto, in Astrophysics and gravitation, Proceedings of the Sixteenth Solvay Conference on Physics, Brussels, Belgium, September 24-28, 1973 (Éditions de l’Université de Bruxelles, Brussels, 1974) pp. 221--267

  48. C.W. Misner, D.H. Sharp, Phys. Rev. B 136, 571 (1964)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  50. S.K. Maurya, Y.K. Gupta, S. Ray, V. Chatterjee, arXiv:1507.01862 [gr-qc] (2015)

  51. N. Straumann, General Relativity and Relativistic Astrophysics (Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1984)

  52. C.G. Böhmer, T. Harko, Class. Quantum Grav. 23, 6479 (2006)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical & Physical Sciences, College of Arts & Science, University of Nizwa, Nizwa, Sultanate of Oman

    S. K. Maurya & Smitha T.T.

  2. Department of Mathematics, Raj Kumar Goel Institute of Technology, 201003, U.P., Ghaziabad, India

    Y. K. Gupta

  3. Department of Mathematics, Jadavpur University, 700032, Kolkata, West Bengal, India

    Farook Rahaman

Authors
  1. S. K. Maurya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. K. Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Smitha T.T.
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Farook Rahaman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. K. Maurya.

Additional information

Communicated by D. Blaschke

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maurya, S.K., Gupta, Y.K., T.T., S. et al. A new exact anisotropic solution of embedding class one. Eur. Phys. J. A 52, 191 (2016). https://doi.org/10.1140/epja/i2016-16191-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/i2016-16191-1

Search

Navigation