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A generalised embedding class one static solution describing anisotropic fluid sphere

  • M. K. Jasim
  • S. K. MauryaEmail author
  • Amina Said Mohammed Al-Sawaii
Original Article
  • 31 Downloads

Abstract

In the present article, the Eiesland condition has been used to obtain a new solution for compact star model by considering a non-singular well behaved gravitational potential of the form \(e^{\lambda (r)}=1+a r ^{2} [1+\tanh (br^{2}+c)]^{n}\) in the framework of anisotropic matter distribution. The solution so obtained is physically acceptable, which is exploited to compare the predicted masses and radii of known compact object as EXO 1785-248 (\(M=1.3M_{\odot }\)) for \(n= 3\) to 15. Moreover, the obtained solution satisfies the causality condition, Herrera cracking criterion, Tolman-Oppenheimer-Volkoff (TOV) equation, and adiabatic index \(\varGamma \) including all energy conditions. It is noted that the velocity of sound is increasing at \(n=3\) and start decreasing when \(n\ge 6\) which shows that the parameter \(n\) plays an important role to describe a well-behaved solution for anisotropic compact object. The moment of inertia \((I)\) is also obtained by Bejger-Haensel formula for \(n=3\) to 15. In addition to that, the maximum mass for the compact star has been discovered via. \(M-R\) curve for different values of \(n\).

Keywords

General Relativity Eiesland condition Compact star 

Notes

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this manuscript.

References

  1. Abreu, H., Hernandez, H., Núñez, L.A.: Class. Quantum Gravity 24, 4631 (2007) ADSCrossRefGoogle Scholar
  2. Bejger, M., Haensel, P.: Astron. Astrophys. 396, 917 (2002) ADSCrossRefGoogle Scholar
  3. Bondi, H.: Proc. R. Soc. Lond. A 281, 39 (1964) ADSCrossRefGoogle Scholar
  4. Bowers, R.L., Liang, E.P.T.: Astrophys. J. 188, 657 (1974) ADSCrossRefGoogle Scholar
  5. Buchdahl, H.A.: Phys. Rev. D 116, 1027 (1959) ADSCrossRefGoogle Scholar
  6. Chan, R., Herrera, L., Santos, N.O.: Mon. Not. R. Astron. Soc. 265, 533 (1993) ADSCrossRefGoogle Scholar
  7. Chattopadhyay, P.K., Paul, B.C.: Pramāna 74, 513 (2010) ADSCrossRefGoogle Scholar
  8. Eddington, A.S.: The Mathematical Theory of Relativity, p. 149. Cambridge University Press, Cambridge (1924) Google Scholar
  9. Eiesland, J.: The group of motion of an Einstein space. Trans. Am. Math. Soc. 27, 213 (1925) MathSciNetzbMATHCrossRefGoogle Scholar
  10. Eisenhart, L.P.: Riemannian Geometry, p. 97. Princeton Univ. Press, Princeton, New Jersey (1925) Google Scholar
  11. Gupta, Y.K., Kumar, J.: Astrophys. Space Sci. 336, 419 (2011) ADSCrossRefGoogle Scholar
  12. Hansraj, S.: Gen. Relativ. Gravit. 4, 125 (2012) ADSMathSciNetCrossRefGoogle Scholar
  13. Harrison, B.K., Thorne, K.S., Wakano, M., Wheeler, J.A.: University of Chicago Press, Chicago (1965) Google Scholar
  14. Herrera, L.: Phys. Lett. A 165, 206 (1992) ADSCrossRefGoogle Scholar
  15. Herrera, L., Ponce de Leon, J.: J. Math. Phys. 26, 2302 (1985) ADSMathSciNetCrossRefGoogle Scholar
  16. Herrera, L., Santos, N.O.: Astrophys. J. 438, 308 (1995) ADSCrossRefGoogle Scholar
  17. Herrera, L., Santos, N.O.: Phys. Rep. 286, 53 (1997) ADSMathSciNetCrossRefGoogle Scholar
  18. Herrera, L., Jimenez, J., Leal, L., Ponce de Leon, J.: J. Math. Phys. 25, 3274–3278 (1984) ADSMathSciNetCrossRefGoogle Scholar
  19. Herrera, L., Di Prisco, A., Ospino, J., Fuenmayor, E.: J. Math. Phys. 42, 2129 (2001) ADSMathSciNetCrossRefGoogle Scholar
  20. Herrera, L., Martin, J., Ospino, J.: J. Math. Phys. 43, 4889 (2002) ADSMathSciNetCrossRefGoogle Scholar
  21. Ivanov, B.V.: Phys. Rev. D 65, 104011 (2002) ADSCrossRefGoogle Scholar
  22. Ivanov, B.V.: Eur. Phys. J. C 78, 332 (2018) ADSCrossRefGoogle Scholar
  23. Jasim, M.K., Maurya, S.K., Gupta, Y.K., Dayanandan, B.: Astrophys. Space Sci. 361, 352 (2016) ADSCrossRefGoogle Scholar
  24. Kaluza, T.: Sitz. Preuss. Acad. Wiss. F 1, 966 (1921) Google Scholar
  25. Karmarkar, K.R.: Proc. Indian Acad. Sci. A 27, 56 (1948) CrossRefGoogle Scholar
  26. Kippenhahn, R., Weigert, A. (eds.): Springer, Berlin (1990) Google Scholar
  27. Klein, O.: Z. Phys. 37, 895 (1926) ADSCrossRefGoogle Scholar
  28. Kohler, M., Chao, K.L.: Z. Naturforsch. 20, 1537 (1965) ADSCrossRefGoogle Scholar
  29. Lake, K.: Phys. Rev. D 67, 104015 (2003) ADSMathSciNetCrossRefGoogle Scholar
  30. Letelier, P.S.: Phys. Rev. D 22, 807 (1980) ADSMathSciNetCrossRefGoogle Scholar
  31. Letelier, P.S.: Nuovo Cimento B 69, 145 (1982) ADSCrossRefGoogle Scholar
  32. Letelier, P.S., Machado, R.: J. Math. Phys. 22, 827 (1981) ADSMathSciNetCrossRefGoogle Scholar
  33. Liddle, A.R., et al.: Class. Quantum Gravity 7, 1009 (1990) ADSCrossRefGoogle Scholar
  34. Maharaj, S.D., Govender, M.: Aust. J. Phys. 0, 959 (1997) ADSCrossRefGoogle Scholar
  35. Maharaj, S.D., Komathiraj, K.: Gen. Relativ. Gravit. 39, 2079 (2007) ADSCrossRefGoogle Scholar
  36. Mak, M.K., Harko, T.: Proc. R. Soc. Lond. A 459, 393–408 (2003) ADSCrossRefGoogle Scholar
  37. Maurya, S.K., Govender, M.: Eur. Phys. J. C 77, 347 (2017a) ADSCrossRefGoogle Scholar
  38. Maurya, S.K., Govender, M.: Eur. Phys. J. C 77, 420 (2017b) ADSCrossRefGoogle Scholar
  39. Maurya, S.K., et al.: Eur. Phys. J. C 75, 389 (2015a) ADSCrossRefGoogle Scholar
  40. Maurya, S.K., Gupta, Y.K., Ray, S., Dayanandan, B.: Eur. Phys. J. C 75, 225 (2015b) ADSCrossRefGoogle Scholar
  41. Maurya, S.K., Gupta, Y.K., Dayanandan, B., Ray, S.: Eur. Phys. J. C 76, 266 (2016a) ADSCrossRefGoogle Scholar
  42. Maurya, S.K., Gupta, Y.K., Smitha, T.T., Rahaman, F.: Eur. Phys. J. A 52, 191 (2016b) ADSCrossRefGoogle Scholar
  43. Maurya, S.K., et al.: Int. J. Mod. Phys. D 26, 1750002 (2017a) ADSCrossRefGoogle Scholar
  44. Maurya, S.K., Ratanpal, B.S., Govender, M.: Ann. Phys. 382, 36 (2017b) ADSCrossRefGoogle Scholar
  45. Maurya, S.K., Banerjee, A., Hansraj, S.: Phys. Rev. D 97, 044022 (2018) ADSMathSciNetCrossRefGoogle Scholar
  46. Pandey, S.N., Sharma, S.P.: Gen. Relativ. Gravit. 14, 113 (1981) ADSCrossRefGoogle Scholar
  47. Pani, P., Berti, E., Cardoso, V., Read, J.: Phys. Rev. D 84, 104035 (2011) ADSCrossRefGoogle Scholar
  48. Pavsic, M., Tapia, V.: (2001). arXiv:gr-qc/0010045
  49. Rayski, J.: Preprint. Dublin Institute for Advance Studies (1976) Google Scholar
  50. Rude, R.: Astrophysics 10, 427 (1972) Google Scholar
  51. Sarkar, N., et al.: Mod. Phys. Lett. A 34, 195013 (2019) Google Scholar
  52. Sawyer, R.F.: Phys. Rev. Lett. 29, 382 (1972) ADSCrossRefGoogle Scholar
  53. Schwarzschild, K.: Sitz. Deut. Akad. Wiss. Math. Phys. Berlin 24, 424 (1916) Google Scholar
  54. Singh, K.N., Pant, N.: Astrophys. Space Sci. 361, 177 (2016) ADSCrossRefGoogle Scholar
  55. Singh, K.N., et al.: Astrophys. Space Sci. 361, 173 (2016a) ADSCrossRefGoogle Scholar
  56. Singh, K.N., et al.: Int. J. Mod. Phys. D 25, 1650099 (2016b) ADSCrossRefGoogle Scholar
  57. Singh, K.N., et al.: Ann. Phys. 377, 256 (2016c) ADSCrossRefGoogle Scholar
  58. Singh, K.N., et al.: Eur. Phys. J. C 77, 100 (2017a) ADSCrossRefGoogle Scholar
  59. Singh, K.N., et al.: Eur. Phys. J. A 53, 21 (2017b) ADSCrossRefGoogle Scholar
  60. Singh, K.N., et al.: Int. J. Mod. Phys. D 27, 1950003 (2018) ADSCrossRefGoogle Scholar
  61. Singh, K.N., et al.: Eur. Phys. J. C 79, 381 (2019) ADSCrossRefGoogle Scholar
  62. Sokolov, A.I.: J. Exp. Theor. Phys. 79, 1137 (1980) Google Scholar
  63. Thirukkanesh, S.: Int. J. Mod. Phys. D 24, 1550002 (2014) ADSCrossRefGoogle Scholar
  64. Zeldovich, Y.B., Novikov, I.D.: Relativistic Astrophysics Stars and Relativity, vol. 1. University of Chicago Press, Chicago (1971) Google Scholar

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© Springer Nature B.V. 2020

Authors and Affiliations

  1. 1.Department of Mathematical & Physical Sciences, College of Arts & ScienceUniversity of NizwaNizwaSultanate of Oman
  2. 2.Department of Mathematics and StatisticsSultan Qaboos UniversityMuscatSultanate of Oman

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