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Stellar filaments with Minkowskian core in the Einstein-\(\Lambda\) gravity

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Abstract.

In this paper, we study the effects of cosmological constant and expansion-free condition on the formulation of exact analytical solutions of relativistic stellar interior. For this purpose, we assume a non-static and non-diagonal cosmic stellar filament filled with anisotropic fluid configurations in a \(\Lambda\)-dominated epoch. The assumption of considering the expansion-free condition has made the system develop a Minkowskian core, which suggests the relevance of our models in the study of cosmological voids. After evaluating the Darmois junction conditions, we have investigated the role of tidal forces in the maintenance of the conformal flat condition. We found that some of our solutions indicate the existence of thin shell at the expansion-free cylindrical hypersurfaces.

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References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. D.N. Spergel et al., Astrophys. J. Suppl. 148, 175 (2003)

    Article  ADS  Google Scholar 

  5. M. Tegmark et al., Astrophys. J. 606, 702 (2004)

    Article  ADS  Google Scholar 

  6. S. Capozziello, Int. J. Mod. Phys. D 11, 483 (2002)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. M.J.S. Houndjo, Int. J. Mod. Phys. D 21, 1250003 (2012)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. I. Ayuso, J.B. Jimenez, A.D.L. Cruz-Dombriz, Phys. Rev. D 91, 104003 (2015)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. S. Nojiri, S.D. Odintsov, Phys. Rev. D 68, 123512 (2003) arXiv:hep-th/0307288

    Article  ADS  Google Scholar 

  15. S. Nojiri, S.D. Odintsov, Phys. Rep. 505, 59 (2011) arXiv:1011.0544 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

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

  17. S. Capozziello, M. De Laurentis, Phys. Rep. 509, 167 (2011) arXiv:1108.6266 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  18. K. Bamba, S. Capozziello, S. Nojiri, S.D. Odintsov, Astrophys. Space Sci. 342, 155 (2012) arXiv:1205.3421 [gr-qc]

    Article  ADS  Google Scholar 

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

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

  21. M.Z. Bhatti, Z. Yousaf, S. Hanif, Phys. Dark Univ. 16, 34 (2017)

    Article  Google Scholar 

  22. Z. Yousaf, M.Z. Bhatti, A. Rafaqat, Int. J. Mod. Phys. D 26, 1750099 (2017)

    Article  ADS  Google Scholar 

  23. M. Cissoko, J.C. Fabris, J. Gariel, G. Le Denmat, N.O. Santos, arXiv:gr-qc/9809057

  24. S.M. Wagh, S.D. Maharaj, Gen. Relativ. Gravit. 31, 975 (1999)

    Article  ADS  Google Scholar 

  25. J.P.S. Lemos, Phys. Lett. A 158, 271 (1991)

    Article  ADS  Google Scholar 

  26. J.P.S. Lemos, Phys. Rev. Lett. 68, 1447 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  27. D. Markovic, S.L. Shapiro, Phys. Rev. D 61, 084029 (2000)

    Article  ADS  Google Scholar 

  28. K. Lake, Phys. Rev. D 62, 027301 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  29. S.S. Deshingkar, S. Jhingan, A. Chamorro, P.S. Joshi, Phys. Rev. D 63, 124005 (2001)

    Article  ADS  Google Scholar 

  30. S.G. Ghosh, Int. J. Mod. Phys. D 14, 707 (2005)

    Article  ADS  Google Scholar 

  31. M.S. Berman, Gen. Relativ. Gravit. 23, 465 (1991)

    Article  ADS  Google Scholar 

  32. A. Pradhan, A. Kumar, Int. J. Mod. Phys. D 10, 291 (2001)

    Article  ADS  Google Scholar 

  33. A. Pradhan, V.K. Yadav, Int. J. Mod. Phys. D 11, 893 (2002)

    Article  ADS  Google Scholar 

  34. T. Harko, M.K. Mak, Gen. Relativ. Gravit. 31, 849 (1999)

    Article  ADS  Google Scholar 

  35. A. Pradhan, P. Pandey, G.P. Singh, R.V. Deshpandey, Spacetime Substance 6, 116 (2005) arXiv:gr-qc/0310023

    Google Scholar 

  36. U. Debnath, S. Nath, S. Chakraborty, Mon. Not. R. Astron. Soc. 369, 1961 (2006)

    Article  ADS  Google Scholar 

  37. L. Herrera, A. Di Prisco, J. Ibáñez, Phys. Rev. D 84, 107501 (2011)

    Article  ADS  Google Scholar 

  38. G.H. Bordbar, S.H. Hendi, B.E. Panah, Eur. Phys. J. Plus 131, 315 (2016)

    Article  Google Scholar 

  39. J.L. Blázquez-Salcedo, J. Kunz, F. Navarro-Lérida, E. Radu, Phys. Rev. D 95, 064018 (2017)

    Article  ADS  Google Scholar 

  40. B. Gwak, D. Ro, arXiv:1610.04847 [gr-qc]

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  43. V.A. Skripkin, Sov. Phys. Dokl. 135, 1183 (1960)

    MathSciNet  Google Scholar 

  44. L. Herrera, N.O. Santos, A. Wang, Phys. Rev. D 78, 084026 (2008)

    Article  ADS  Google Scholar 

  45. L. Herrera, G. Le Denmat, N.O. Santos, Phys. Rev. D 79, 087505 (2009)

    Article  ADS  Google Scholar 

  46. M. Sharif, Z. Yousaf, Int. J. Mod. Phys. D 21, 1250095 (2012)

    Article  ADS  Google Scholar 

  47. L. Herrera, N.O. Santos, G. Le Denmat, Gen. Relativ. Gravit. 44, 1143 (2012)

    Article  ADS  Google Scholar 

  48. A. Di Prisco, L. Herrera, J. Ospino, N.O. Santos, V.M. Viña-Cervantes, Int. J. Mod. Phys. D 20, 2351 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  51. L. Herrera, Entropy 19, 110 (2017)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  53. K.S. Thorne, Phys. Rev. B 138, 251 (1965)

    Article  ADS  Google Scholar 

  54. H. Chao-Guang, Acta Phys. Sin. 4, 617 (1995)

    ADS  Google Scholar 

  55. G. Darmois, Memorial des Sciences Mathematiques (Gautheir-Villars) Fasc. 25 (1965)

  56. L. Herrera, N.O. Santos, G. Le Denmat, Class. Quantum Grav. 27, 135017 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  61. P.C. Myers, Astrophys. J. 764, 140 (2013)

    Article  ADS  Google Scholar 

  62. P.C. Breysse, M. Kamionkowski, A. Benson, Mon. Not. R. Astron. Soc. 437, 2675 (2014)

    Article  ADS  Google Scholar 

  63. Y. Birnboim, D. Padnos, E. Zinger, Astrophys. J. Lett. 832, L4 (2016)

    Article  ADS  Google Scholar 

  64. Z. Yousaf, M.Z. Bhatti, Mon. Not. R. Astron. Soc. 458, 1785 (2016) arXiv:1612.02325 [physics.gen-ph]

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

  67. L. Herrera, N.O. Santos, Gen. Relativ. Gravit. 27, 1071 (1997)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  69. Z. Yousaf, M.Z. Bhatti, A. Rafaqat, Int. J. Mod. Phys. D 26, 1750099 (2017)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  71. M. Petri, arXiv:gr-qc/03060673

  72. M. Petri, arXiv:gr-qc/0405007

  73. M. Petri, arXiv:gr-qc/0306063

  74. R. Pim, K. Lake, Astrophys. J. 330, 625 (1988)

    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

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  1. Z. Yousaf
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Yousaf, Z. Stellar filaments with Minkowskian core in the Einstein-\(\Lambda\) gravity. Eur. Phys. J. Plus 132, 276 (2017). https://doi.org/10.1140/epjp/i2017-11547-0

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