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Dynamical instability of spherical anisotropic sources in \(\mathrm{ f(R,T,R_{\mu\nu}T^{\mu\nu})}\) gravity

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Abstract.

In this paper, we study the effects of modification of gravity on the problem of dynamical instability of the spherical relativistic anisotropic interiors. We have considered non-zero influence of expansion scalar throughout during the evolutionary phases of spherical geometry that led to the use of the fluid stiffness parameter. The modified hydrostatic equation for the stellar anisotropic matter distributions is constructed and then solved by using a radial perturbation scheme. Such a differential equation can be further used to obtain instability constraints at both weak field and post-Newtonian approximations after considering a particular Harrison-Wheeler equation of state. This approach allows us to deal with the effects of usual and effective matter variables on the stability exotic stellar of self-gravitating structures.

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References

  1. S. Weinberg, Rev. Mod. Phys. 61, 1 (1989)

    Article  ADS  Google Scholar 

  2. P.J.E. Peebles, B. Ratra, Rev. Mod. Phys. 75, 559 (2003)

    Article  ADS  Google Scholar 

  3. V. Husain, B. Qureshi, Phys. Rev. Lett. 116, 061302 (2016)

    Article  ADS  Google Scholar 

  4. D. Pietrobon, A. Balbi, D. Marinucci, Phys. Rev. D 74, 043524 (2006)

    Article  ADS  Google Scholar 

  5. T. Giannantonio et al., Phys. Rev. D 74, 063520 (2006)

    Article  ADS  Google Scholar 

  6. A.G. Riess et al., Astrophys. J. 659, 98 (2007)

    Article  ADS  Google Scholar 

  7. A. Qadir, H.W. Lee, K.Y. Kim, Int. J. Mod. Phys. D 26, 1741001 (2017)

    Article  ADS  Google Scholar 

  8. S. Nojiri, S.D. Odintsov, Int. J. Geom. Methods Mod. Phys. 4, 115 (2007) arXiv:hep-th/0601213

    Article  MathSciNet  Google Scholar 

  9. T.P. Sotirou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010)

    Article  ADS  Google Scholar 

  10. S. Nojiri, S.D. Odintsov, Phys. Rep. 505, 59 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  11. S. Capozziello, M.D. Laurentis, Phys. Rep. 509, 167 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  12. S. Capozziello, V. Faraoni, Beyond Einstein Gravity (Springer, Dordrecht, 2010)

  13. K. Bamba, S. Capozziello, S. Nojiri, S.D. Odintsov, Astrophys. Space Sci. 342, 155 (2012)

    Article  ADS  Google Scholar 

  14. A. de la Cruz-Dombriz, D. Sáez-Gómez, Entropy 14, 1717 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  15. A. Joyce, B. Jain, J. Khoury, M. Trodden, Phys. Rep. 568, 1 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  16. K. Koyama, arXiv:1504.04623 [astro-ph.CO]

  17. K. Bamba, S. Nojiri, S.D. Odintsov, arXiv:1302.4831 [gr-qc]

  18. K. Bamba, S.D. Odintsov, arXiv:1402.7114 [hep-th]

  19. K. Bamba, S.D. Odintsov, Symmetry 7, 220 (2015) arXiv:1503.00442 [hep-th]

    Article  MathSciNet  Google Scholar 

  20. Z. Yousaf, K. Bamba, M.Z. Bhatti, Phys. Rev. D 95, 024024 (2017) arXiv:1701.03067 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  21. S. Nojiri, S.D. Odintsov, Phys. Rev D 68, 123512 (2003)

    Article  ADS  Google Scholar 

  22. M. Sharif, Z. Yousaf, Gen. Relativ. Gravit. 47, 48 (2015)

    Article  ADS  Google Scholar 

  23. M. Sharif, Z. Yousaf, Can. J. Phys. 93, 905 (2015)

    Article  ADS  Google Scholar 

  24. M.Z. Bhatti, Z. Yousaf, Int. J. Mod. Phys. D 26, 1750029 (2017)

    Article  ADS  Google Scholar 

  25. M.Z. Bhatti, Z. Yousaf, Int. J. Mod. Phys. D 26, 1750045 (2017)

    Article  ADS  Google Scholar 

  26. M.Z. Bhatti, Z. Yousaf, Eur. Phys. J. C 76, 219 (2016) arXiv:1604.01395 [gr-qc]

    Article  ADS  Google Scholar 

  27. Z. Yousaf, Eur. Phys. J. Plus 132, 71 (2017)

    Article  Google Scholar 

  28. T. Harko, F.S.N. Lobo, S. Nojiri, S.D. Odintsov, Phys. Rev. D 84, 024020 (2011)

    Article  ADS  Google Scholar 

  29. Z. Yousaf, M.Z. Bhatti, Eur. Phys. J. C 76, 267 (2016) arXiv:1604.06271 [physics.gen-ph]

    Article  ADS  Google Scholar 

  30. M. Sharif, Z. Yousaf, Astrophys. Space Sci. 354, 471 (2014)

    Article  ADS  Google Scholar 

  31. Z. Yousaf, K. Bamba, M.Z. Bhatti, Phys. Rev. D 95, 024024 (2017) arXiv:1701.03067 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  32. S. Nojiri, S.D. Odintsov, Phys. Lett. B 631, 1 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  33. S.D. Odintsov, D. Sáez-Gómez, Phys. Lett. B 725, 437 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  34. Z. Haghani, T. Harko, F.S.N. Lobo, H.R. Sepangi, S. Shahidi, Phys. Rev. D 88, 044023 (2013)

    Article  ADS  Google Scholar 

  35. Z. Yousaf, M.Z. Bhatti, U. Farwa, Class. Quantum Grav. 34, 145002 (2017)

    Article  ADS  Google Scholar 

  36. S. Chandrasekhar, Astrophys. J. 140, 417 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  37. L. Herrera, N.O. Santos, G. Le Denmat, Mon. Not. R. Astron. Soc. 237, 257 (1989)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  39. R. Chan, L. Herrera, N.O. Santos, Mon. Not. R. Astron. Soc. 267, 637 (1994)

    Article  ADS  Google Scholar 

  40. R. Chan, Mon. Not. R. Astron. Soc. 316, 588 (2000)

    Article  ADS  Google Scholar 

  41. L. Herrera, G. Le Denmat, N.O. Santos, Gen. Relativ. Gravit. 44, 1144 (2012)

    ADS  Google Scholar 

  42. Z. Haghani, T. Harko, F.S.N. Lobo, H.R. Sepangi, S. Shahidi, Phys. Rev. D 88, 044023 (2013)

    Article  ADS  Google Scholar 

  43. I. Ayuso et al., Phys. Rev. D 91, 104003 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  44. E. Elizalde, S.I. Vacaru, Gen. Relativ. Gravit. 47, 64 (2015)

    Article  ADS  Google Scholar 

  45. Z. Yousaf, M.Z. Bhatti, U. Farwa, Mon. Not. R. Astron. Soc. 464, 4509 (2017)

    Article  ADS  Google Scholar 

  46. Z. Yousaf, M.Z. Bhatti, U. Farwa, Eur. Phys. J. C 77, 359 (2017) arXiv:1705.06975 [physics.gen-ph]

    Article  ADS  Google Scholar 

  47. R. Garattini, J. Phys. Conf. Ser. 174, 012066 (2009)

    Article  Google Scholar 

  48. A.H. Ziaie, K. Atazadeh, S.M.M. Rasouli, Gen. Relativ. Gravit. 43, 2943 (2011)

    Article  ADS  Google Scholar 

  49. S.G. Ghosh, S.D. Maharaj, Phys. Rev. D 85, 124064 (2012)

    Article  ADS  Google Scholar 

  50. B.M. Núñez, J.A.R. Cembranos, Á. de la Cruz-Dombriz, AIP Conf. Proc. 1458, 491 (2012) arXiv:1210.7968 [gr-qc]

    Article  ADS  Google Scholar 

  51. L. Reverberi, Phys. Rev. D 87, 084005 (2013)

    Article  ADS  Google Scholar 

  52. Z. Yousaf, Eur. Phys. J. Plus 132, 71 (2017)

    Article  Google Scholar 

  53. Z. Yousaf, Eur. Phys. J. Plus 132, 276 (2017)

    Article  Google Scholar 

  54. E.V. Arbuzova, A.D. Dolgov, L. Reverberi, Astropart. Phys. 54, 44 (2014)

    Article  ADS  Google Scholar 

  55. M. Sharif, Z. Yousaf, Eur. Phys. J. C 75, 58 (2015)

    Article  ADS  Google Scholar 

  56. M.Z. Bhatti, Eur. Phys. J. Plus 131, 428 (2016)

    Article  Google Scholar 

  57. M. Sharif, Z. Yousaf, Eur. Phys. J. C 75, 194 (2015) arXiv:1504.04367v1 [gr-qc]

    Article  ADS  Google Scholar 

  58. M. Fathi, M. Mohseni, Eur. Phys. J. Plus 131, 360 (2016)

    Article  Google Scholar 

  59. Z. Yousaf, M.Z. Bhatti, Mon. Not. R. Astron. Soc. 458, 1785 (2016)

    Article  ADS  Google Scholar 

  60. S. Chakrabarti, N. Banerjee, Eur. Phys. J. Plus 131, 144 (2016)

    Article  Google Scholar 

  61. M. Sharif, Z. Yousaf, Int. J. Theor. Phys. 55, 470 (2016)

    Article  Google Scholar 

  62. J.-Q. Guo, P.S. Joshi, Phys. Rev. D 94, 044063 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  63. Z. Yousaf, K. Bamba, M.Z. Bhatti, Phys. Rev. D 93, 124048 (2016) arXiv:1606.00147 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  64. C.-Y. Zhang, Z.-Y. Tang, B. Wang, Phys. Rev. D 94, 104013 (2016) arXiv:1608.04836 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  65. S. Satin, D. Malafarina, P.S. Joshi, Int. J. Mod. Phys. D 25, 1650023 (2016)

    Article  ADS  Google Scholar 

  66. G. Abbas, M. Tahir, Eur. Phys. J. C 77, 537 (2017) arXiv:1707.08472 [gr-qc]

    Article  ADS  Google Scholar 

  67. K.S. Adhav, Astrophys. Space Sci. 339, 365 (2012)

    Article  ADS  Google Scholar 

  68. S.K. Sahu, S.K. Tripathy, P.K. Sahoo, A. Nath, Chin. J. Phys. 55, 862 (2017)

    Article  Google Scholar 

  69. P.K. Sahoo, P. Sahoo, B.K. Bishi, S. Aygün, Mod. Phys. Lett. 32, 1750105 (2017)

    Article  ADS  Google Scholar 

  70. L. Herrera, A. Di Prisco, J.L. Hernández-Pastora, N.O. Santos, Phys. Lett. A 237, 113 (1998)

    Article  ADS  Google Scholar 

  71. L. Herrera, Int. J. Mod. Phys. D 20, 1689 (2011)

    Article  ADS  Google Scholar 

  72. L. Herrera, N.O. Santos, Phys. Rev. D 70, 084004 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  73. L. Herrera, A. Di Prisco, W. Barreto, Phys. Rev. D 73, 024008 (2006)

    Article  ADS  Google Scholar 

  74. L. Herrera, Int. J. Mod. Phys. D 15, 2197 (2006)

    Article  ADS  Google Scholar 

  75. S. Capozziello, M. De Laurentis, S.D. Odintsov, A. Stabile, Phys. Rev. D 83, 064004 (2011)

    Article  ADS  Google Scholar 

  76. S. Capozziello, M. De Laurentis, I. De Martino, M. Formisano, S.D. Odintsov, Phys. Rev. D 85, 044022 (2012)

    Article  ADS  Google Scholar 

  77. J.A.R. Cembranos, Á. de la Cruz-Dombriz, B.M. Núñez, J. Cosmol. Astropart. Phys. 04, 021 (2012)

    Article  ADS  Google Scholar 

  78. M. Sharif, Z. Yousaf, Eur. Phys. J. C 75, 194 (2015) arXiv:1504.04367v1 [gr-qc]

    Article  ADS  Google Scholar 

  79. M. Sharif, Z. Yousaf, Astrophys. Space Sci. 357, 49 (2015)

    Article  ADS  Google Scholar 

  80. M. Sharif, Z. Yousaf, Astrophys. Space Sci. 351, 351 (2014)

    Article  ADS  Google Scholar 

  81. M.Z. Bhatti, Z. Yousaf, Eur. Phys. J. C 76, 219 (2016) arXiv:1604.01395 [gr-qc]

    Article  ADS  Google Scholar 

  82. M.Z. Bhatti, Z. Yousaf, Ann. Phys. 387, 253 (2017)

    Article  ADS  Google Scholar 

  83. M.Z. Bhatti, Z. Yousaf, S. Hanif, Phys. Dark Universe 16, 34 (2017)

    Article  ADS  Google Scholar 

  84. Z. Yousaf, K. Bamba, M.Z. Bhatti, Phys. Rev. D 93, 064059 (2016) arXiv:1603.03175 [gr-qc]

    Article  ADS  Google Scholar 

  85. E.H. Baffou, M.J.S. Houndjo, J. Tossa, Astrophys. Space Sci. 361, 376 (2016) arXiv:1608.03273[gr-qc]

    Article  ADS  Google Scholar 

  86. T. Harko, F.S.N. Lobo, S. Nojiri, S.D. Odintsov, Phys. Rev. D 84, 024020 (2011)

    Article  ADS  Google Scholar 

  87. C. Misner, D. Sharp, Phys. Rev. D 136, B571 (1964)

    Article  ADS  Google Scholar 

  88. B.K. Harrison, K.S. Throne, M. Wakano, J.A. Wheeler, Gravitation Theory and Gravitational Collapse (University of Chicago Press, 1965)

  89. Z. Yousaf, M. Sharif, M. Ilyas, M.Z. Bhatti, Eur. Phys. J. C 77, 691 (2017) arXiv:1710.05717 [gr-qc]

    Article  ADS  Google Scholar 

  90. M.Z. Bhatti, M. Sharif, Z. Yousaf, M. Ilyas, Int. J. Mod. Phys. D 27, 1850044 (2018)

    Article  ADS  Google Scholar 

  91. Z. Yousaf, M.Z. Bhatti, M. Ilyas, Eur. Phys. J. C 78, 307 (2018) arXiv:1804.04953 [physics.gen-ph]

    Article  ADS  Google Scholar 

  92. M. Sharif, Z. Yousaf, Astropart. Phys. 56, 19 (2014)

    Article  ADS  Google Scholar 

  93. C.M. Will, Theory and Experiment in Gravitational Physics (Cambridge Univ. Press, 1993)

  94. N. Straumann, General Relativity: with Aplication to Astrophysics (Springer, 2004)

  95. M. Sharif, Z. Yousaf, Astrophys. Space Sci. 355, 317 (2015)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, Quaid-i-Azam Campus, 54590, Lahore, Pakistan

    Z. Yousaf, M. Z. Bhatti & U. Farwa

  2. Division of Human Support System, Faculty of Symbiotic Systems Science, Fukushima University, 960-1296, Fukushima, Japan

    Kazuharu Bamba

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  1. Z. Yousaf
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  2. Kazuharu Bamba
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  3. M. Z. Bhatti
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  4. U. Farwa
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Correspondence to Z. Yousaf.

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Communicated by G. Torrieri

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Yousaf, Z., Bamba, K., Bhatti, M.Z. et al. Dynamical instability of spherical anisotropic sources in \(\mathrm{ f(R,T,R_{\mu\nu}T^{\mu\nu})}\) gravity. Eur. Phys. J. A 54, 122 (2018). https://doi.org/10.1140/epja/i2018-12556-8

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