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Behavior of anisotropic fluids with Chaplygin equation of state in Buchdahl spacetime

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Abstract

In the present study we have proposed a new model of an anisotropic compact star which admits the Chaplygin equation of state. For this purpose, we consider Buchdahl ansatz. We obtain the solution of proposed model in closed form which is non-singular, regular and well-behaved. In addition to this, we show that the model satisfies all the energy conditions and maintains the hydrostatic equilibrium equation. This model represents compact stars like PSR B0943+10, Her X-1 and SAX J1808.4-3658 to a very good approximate.

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References

  1. Schwarzschild, K.: Sitz. Deut. Akad. Wiss. Math.Phys. Berlin 24, 424 (1916)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Sharma, R., Karmakar, S., Mukherjee, S.: Int. J. Mod. Phys. D 15, 405 (2006)

    Article  ADS  Google Scholar 

  4. Ruderman, R.: Rev. Astr. Astrophys. 10, 427 (1972)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Ivanov, B.V.: Eur. Phys. J. C 77, 1–12 (2017)

    Article  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  8. Kippenhahn, R., Weigert, A., Weiss, A.: Stellar Structure and Evolution, vol. 192. Springer-Verlag, Berlin (1990)

    Book  MATH  Google Scholar 

  9. Sokolov, A.I., et al.: Sov. Phys. JETP 52, 575 (1980)

    ADS  Google Scholar 

  10. Sawyer, R.F.: Phys. Rev. Lett. 29, 382 (1972)

    Article  ADS  Google Scholar 

  11. Krori, K.D., Borgohain, P., Devi, R.: Can. J. Phys. 62, 239 (1984)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Prasad, A.K. , Kumar, J.: arXiv:2103.12583 (2021)

  14. Maurya, S.K., Gupta, Y.K., Dayanandan, B., Jasim, M.K., Al-Jamel, A.: Int. J. Mod. Phys. D 26, 1750002 (2017)

    Article  ADS  Google Scholar 

  15. Paul, B.C., Deb, R.: Astrophys. Space Sci. 354, 421 (2014)

    Article  ADS  Google Scholar 

  16. Maurya, S.K.: Eur. Phys. J. C 79, 1–15 (2019)

    Article  ADS  Google Scholar 

  17. Maurya, S.K., Maharaj, S.D., Kumar, J., Prasad, A.K.: Gen. Relativ. Gravit. 51, 86 (2019)

    Article  ADS  Google Scholar 

  18. Prasad, A.K., Kumar, J., Maurya, S.K., Dayanandan, B.: Astrophys. Space Sci. 364, 66 (2019)

    Article  ADS  Google Scholar 

  19. Thirukkanesh, S., Maharaj, S.D.: Class. Quantum Gravity 25, 235001 (2008)

    Article  ADS  Google Scholar 

  20. Leyton, Y.G., Javaid, H., Rocha, L.S., Ortiz, F.T.: Phys. Scr. 96, 025001 (2020)

    Article  Google Scholar 

  21. Singh, K.N., Ali, A., Rahaman, F., Nasri, S.: Phys. Dark Univ. 29, 100575 (2020)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. Ngubelanga, A.S., Maharaj, S.D., Ray, S.: Astrophys. Space Sci. 357, 1–9 (2015)

    Article  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  25. Herrera, L., Barreto, W.: Phys. Rev. D 87, 087303 (2013)

    Article  ADS  Google Scholar 

  26. Rahaman, F., Ray, S., Jafry, A.K., Chakraborty, K.: Phys. Rev. D 82, 104055 (2010)

    Article  ADS  Google Scholar 

  27. Herrera, L., Fuenmayor, E., Leon, P.: Phys. Rev. D 93, 024047 (2016)

    Article  MathSciNet  ADS  Google Scholar 

  28. Lobo, S.N.F.: Class. Quantum Gravity 23, 1525 (2006)

    Article  ADS  Google Scholar 

  29. Azam, M., Mardan, S.A., Noureen, I., Rehman, M.A.: Eur. Phys. J. C 76, 1–9 (2016)

    Article  ADS  Google Scholar 

  30. Maedan, S.: Prog. Theor. Exp. Phys. 2020, 033B07 (2020)

    Article  Google Scholar 

  31. Otto, K., Oertel, M., Schaefer, B.J.: Phys. Rev. D 101, 103021 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  32. Koliogiannis, P.S., Moustakidis, Ch.C.: Phys. Rev. C 101, 015805 (2020)

    Article  ADS  Google Scholar 

  33. Ortiz, F.T., Malaver, M., Rincón, A., Leyton, Y.G.: Eur. Phys. J. C 80, 1–13 (2020)

    Article  Google Scholar 

  34. Bento, M.C., Bertolami, O., Sen, A.A.: Phys. Rev. D 66, 043507 (2002)

    Article  ADS  Google Scholar 

  35. Kamenshchik, A., Moschella, U., Pasquier, V.: Phys. Lett. B 511, 265 (2001)

    Article  ADS  Google Scholar 

  36. Farnes, J.S.: A & A 620, A92 (2018)

    Article  ADS  Google Scholar 

  37. Rahaman, F., Ray, S., Jafry, A.K., Chakraborty, K.: Phys. Rev. D 82, 104055 (2010)

    Article  ADS  Google Scholar 

  38. Bhar, P.: Astrophys. Space Sci. 359, 41 (2015)

    Article  ADS  Google Scholar 

  39. Benaoum, H.B.: arXiv:hep-th/0205140, (2002)

  40. Kumar, J., Gupta, Y.K.: Astrophys. Space Sci. 345(2), 331–337 (2013)

    Article  ADS  Google Scholar 

  41. Kumar, J., Prasad, A.K., Maurya, S.K., Banerjee, A.: Eur. Phys. J. C 78(7), 1–11 (2018)

    Article  Google Scholar 

  42. Kumar, J., Maurya, S.K., Prasad, A.K., Banerjee, A.: J. Cosmol. Astropart. Phys. 2019(11), 005 (2019)

    Article  Google Scholar 

  43. Prasad, A.K., Kumar, J.: Astrophys. Space Sci. 366(3), 1–14 (2021)

    Article  MathSciNet  Google Scholar 

  44. Prasad, A.K., Kumar, J., Kumar, A.: arXiv preprint arXiv:1911.12974, (2019)

  45. Maurya, S.K., Banerjee, A., Jasim, M.K., Kumar, J., Prasad, A.K., Pradhan, A.: Phys. Rev. D 99(4), 044029 (2019)

    Article  MathSciNet  ADS  Google Scholar 

  46. Maurya, S.K., Banerjee, A., Tello-Ortiz, F.: Phys. Dark Univ. 27, 100438 (2020)

    Article  Google Scholar 

  47. Kumar, J., Singh, H.D., Prasad, A.K.: arXiv preprint arXiv:2106.12560, (2021)

  48. Vaidya, P.C., Tikekar, R.: J. Astrophys. Astron. 3, 325 (1982)

    Article  ADS  Google Scholar 

  49. Israel, W.: Nuovo Cim. B 44, 1 (1966)

    Article  ADS  Google Scholar 

  50. Darmois, G.: Memorial des Sciences Mathematiques. Fasc.Gauthier-Villars, Paris (1927)

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  53. Yue, Y.L., Cui, X.H., Xu, R.X.: Astrophys. J. Lett. 649, L95 (2006)

    Article  ADS  Google Scholar 

  54. Abubekerov, M.K., Antokhina, E.A., Cherepashchuk, A.M., Shimanskii, V.V.: Astron. Rep. 52, 379 (2008)

    Article  ADS  Google Scholar 

  55. Elebert, P., et al.: Mon. Not. R. Astron. Soc. 395, 884 (2009)

    Article  ADS  Google Scholar 

  56. Rej, P., Bhar, P.: Astrophys. Space Sci. 366, 35 (2021)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  58. Maurya, S.K., et al.: Phys. Rev. D 99, 044029 (2019)

    Article  MathSciNet  ADS  Google Scholar 

  59. Gupta, Y.K., Kumar, M.: Astrophys. Space Sci. 299, 43 (2005)

    Article  ADS  Google Scholar 

  60. Gupta, Y.K., Jasim, M.K.: Astrophys. Space Sci. 283, 337 (2003)

    Article  ADS  Google Scholar 

  61. Gasperini, M., Veneziano, G.: Phys. Rep. 373, 1 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  62. de Leon, Ponce: J. Gen. Relat. Gravit. 25, 1123 (1993)

    Article  ADS  Google Scholar 

  63. Visser, M.: Lorentzian Wormholes. Springer, Berlin (1996)

    Google Scholar 

  64. Maurya, S.K., Ortiz, F.T.: Eur. Phys. J. C 79, 85 (2019)

    Article  ADS  Google Scholar 

  65. Heintzmann, H., Hillebrandt, W.: Astron. Astrophys. 38, 51 (1975)

    ADS  Google Scholar 

  66. Moustakidis, C.C.: Gen. Relativ. Gravit. 49(5), 68 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  67. Tello-Ortiz, F., Maurya, S.K., Gomez-Leyton, Y.: Eur. Phys. J. C 80(4), 1–14 (2020)

    Article  Google Scholar 

  68. Maurya, S.K., Nag, R.: Eur. Phys. J. Plus 136(6), 1–34 (2021)

    Article  Google Scholar 

  69. Bondi, H.: Mon. Not. R. Astron. Soc. 281, 39 (1964)

    MathSciNet  Google Scholar 

  70. Harrison, B..K.., et al.: Gravitational Theory and Gravitational Collapse. University of Chicago Press, Chicago (1965)

    Google Scholar 

  71. Zeldovich, Y.. B., Novikov, I.. D.: Relativistic Astrophysics Vol 1: Stars and Relativity. University of Chicago Press, Chicago (1971)

    Google Scholar 

  72. Mak, M.K., Harko, T.: Proc. R. Soc. A 459, 393 (2003)

    Article  ADS  Google Scholar 

  73. Maurya, S.K., Al Aamri, A.M., Al Aamri, A.K., Nag, R.: Eur. Phys. J. C 81(8), 1–21 (2021)

    Google Scholar 

  74. Straumann, N.: General Relativity and Relativistic Astrophysics, p. 43. Springer, Berlin (1984)

    Book  Google Scholar 

  75. Karmakar, S., Mukherjee, S., Sharma, R., Maharaj, S.D.: Pramana 68, 881 (2007)

    Article  ADS  Google Scholar 

  76. Barraco, D.E., Hamity, V.H., Gleiser, R.J.: Phys. Rev. D 67, 064003 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  77. Boehmer, C.G., Harko, T.: Class. Quantum Gravity 23, 6479 (2006)

    Article  ADS  Google Scholar 

  78. Bejger, M., Haensel, P.: A & A 396, 917 (2002)

    Article  ADS  Google Scholar 

  79. Ortiz, F.T., et al.: Eur. Phys. J. C 79, 1–14 (2019)

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank Council of Scientific & Industrial Research (CSIR), India for financial support. The authors are also thankful to Central University of Jharkhand, India for kind support.

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Prasad, A.K., Kumar, J. & Sarkar, A. Behavior of anisotropic fluids with Chaplygin equation of state in Buchdahl spacetime. Gen Relativ Gravit 53, 108 (2021). https://doi.org/10.1007/s10714-021-02883-3

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