Advertisement

A new generalised solution to generate anisotropic compact star models in the Karmarkar space-time manifold

  • Pratibha FuloriaEmail author
Regular Article - Theoretical Physics
  • 28 Downloads

Abstract.

In the present article a new generalised solution is obtained for anisotropic matter configuration using Karmarkar’s condition. The solution is used to model the interior structure of anisotropic relativistic objects as it satisfies all necessary physical conditions. The pressure, density and metric potentials are free from any singularities and exhibit well behaved nature inside the anisotropic fluid sphere. The TOV equation is well maintained within the stellar configuration and all energy conditions hold good. The causality condition is well satisfied for our stellar models and stability of compact star models is further verified via Herrera’s cracking method. Harrison-Zeldovich-Novikov criterion for stability is also satisfied by our model. The adiabatic index is greater than \(\frac{4}{3}\) throughout the stellar interior and the compactification factor also lies within the Buchdahl limit i.e.\(M/R \le 4/9\). We investigate the models for two compact stars PSRJ0348+0432 and SAX J1808.4-3658 within the framework of the general theory of relativity. The estimated mass and radius are in close agreement with the observational data. we extensively study the solutions corresponding to compact star PSRJ0348+0432 for \( n = 0, 1, 2, 3, 4, 4.5\) and the detailed graphical analysis is provided to substantiate the viability of the compact star model. One specific feature of our solution is that for large values of n, i.e. for \( n > 5\) solution reduces to Finch and Skea type solution.

References

  1. 1.
    M. Alford, M. Braby, M.W. Paris, S. Reddy, Astrophys. J. 629, 969 (2005)ADSGoogle Scholar
  2. 2.
    A. Drago, A. Lavango, G. Pagliara, Phys. Rev. D 89, 043014 (2014)ADSGoogle Scholar
  3. 3.
    R. Ruderman, Rev. Astron. Astrophys. 10, 427 (1972)ADSGoogle Scholar
  4. 4.
    F. Weber, Pulsars as Astrophysical Observatories for Nuclear and Particle Physics (Institute of Physics, Bristol, 1999)Google Scholar
  5. 5.
    A.I. Sokolov, J. Exp. Theor. Phys. 79, 1137 (1980)Google Scholar
  6. 6.
    R.F. Sawyer, Phys. Rev. Lett. 29, 382 (1972)ADSGoogle Scholar
  7. 7.
    K.R. Karmarkar, Proc. Indian Acad. Sci. 27, 56 (1948)Google Scholar
  8. 8.
    S.N. Pandey, S.P. Sharma, Gen. Relativ. Grav. 14, 113 (1981)ADSGoogle Scholar
  9. 9.
    K. Schwarzschild, Sitz. Deut. Akad. Wiss. Math. Phys. Berlin 24, 424 (1916)Google Scholar
  10. 10.
    K.N. Singh et al., Astrophys. Space Sci. 361, 173 (2016b)ADSGoogle Scholar
  11. 11.
    K.N. Singh et al., Int. J. Mod. Phys. D 25, 1650099 (2016c)ADSGoogle Scholar
  12. 12.
    K.N. Singh, N. Pant, Indian J. Phys. 90, 843 (2016a)ADSGoogle Scholar
  13. 13.
    K.N. Singh, N. Pant, Astrophys. Space Sci. 361, 177 (2016b)ADSGoogle Scholar
  14. 14.
    R. Sharma, B.S. Ratanpal, arXiv:1307.1439v1 (2013)Google Scholar
  15. 15.
    M. Malaver, Front. Math. Appl. 1, 9 (2014)Google Scholar
  16. 16.
    M. Malaver, Int. J. Mod. Phys. Appl. 2, 1 (2015)Google Scholar
  17. 17.
    F.S.N. Lobo, Class. Quantum Grav. 23, 1525 (2006)ADSGoogle Scholar
  18. 18.
    R. Sharma, S.D. Maharaj, Mon. Not. R. Astron. Soc. 375, 1265 (2007)ADSGoogle Scholar
  19. 19.
    K. Komathiraj, S.D. Maharaj, Int. J. Mod. Phys. D 16, 1803 (2007)ADSGoogle Scholar
  20. 20.
    Piyali Bhar, Muhmmad Hasan Murad, Astrophys. Space Sci. 361, 334 (2016)ADSGoogle Scholar
  21. 21.
    Piyali Bhar, Astrophys. Space Sci. 359, 41 (2015)ADSGoogle Scholar
  22. 22.
    Rahaman, S. Ray, A.K. Jafry, K. Chakraborty, Phys. Rev. D 82, 104055 (2010)ADSGoogle Scholar
  23. 23.
    S. Thirukkanesh, F.C. Ragel, Pramana J. Phys. 78, 687 (2012)ADSGoogle Scholar
  24. 24.
    R. Tikekar, V.O. Thomas, Pramana J. Phys. 52, 237 (1999)ADSGoogle Scholar
  25. 25.
    R. Tikekar, K. Jotania, Pramana J. Phys. 68, 397 (2007)ADSGoogle Scholar
  26. 26.
    K.N. Singh et al., Mod. Phys. Lett. A 32, 1750093 (2017)ADSGoogle Scholar
  27. 27.
    S.K. Maurya, Eur. Phys. J. A 53, 89 (2017)ADSGoogle Scholar
  28. 28.
    Ksh. Newton Singh, Neeraj Pant, Eur. Phys. J. C 76, 524 (2016)ADSGoogle Scholar
  29. 29.
    L. Herrera, Phys. Lett. A 165, 206 (1992)ADSGoogle Scholar
  30. 30.
    H. Abreu et al., Class. Quantum Grav. 24, 4631 (2007)ADSMathSciNetGoogle Scholar
  31. 31.
    H. Heintzmann, W. Hillebrandt, Astron. Astrophys. 38, 51 (1975)ADSGoogle Scholar
  32. 32.
    L. Herrera et al., Astrophys. J. 234, 1094 (1979)ADSGoogle Scholar
  33. 33.
    R. Chan et al., Mon. Not. R. Astron. Soc. 265, 533 (1993)ADSGoogle Scholar
  34. 34.
    B.K. Harrison, Gravitational Theory and Gravitational Collapse (University of Chicago Press, 1965)Google Scholar
  35. 35.
    Ya.B. Zeldovich, I.D. Novikov, Relativistic Astrophysics, Vol. 1, Stars and Relativity (University of Chicago Press, 1971)Google Scholar
  36. 36.
    S. Bhattacharyya, Astron. Astrophys. arXiv:astro-ph/0112175v1 (2001)Google Scholar
  37. 37.
    T.M. Darias et al., Mon. Not. R. Astron. Soc. 394, L136 (2009)ADSGoogle Scholar
  38. 38.
    M.R. Finch, J.E.F. Skea, Class. Quantum Grav. 6, 467 (1989)ADSGoogle Scholar
  39. 39.
    L. Herrera, J. Ospino, A. Di Prisco, Phys. Rev. D 77, 027502 (2008)ADSMathSciNetGoogle Scholar

Copyright information

© SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Physics DepartmentS.S.J. CampusAlmoraIndia

Personalised recommendations