Research ArticleNo Access

Models of non-static and inhomogeneous gravitating source in Rastall gravity

G. Abbas

Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur-63100, Pakistan

E-mail Address: ghulamabbas@iub.edu.pk

Corresponding author.

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M. Tahir

https://orcid.org/0000-0002-5293-3350

Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur-63100, Pakistan

E-mail Address: tmuhammad0064@gmail.com

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, and

M. R. Shahzad

Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur-63100, Pakistan

E-mail Address: rezwan.chaudhery@gmail.com

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https://doi.org/10.1142/S0219887821500420Cited by:7 (Source: Crossref)

Abstract

In this paper, we have explored the non-static anisotropic gravitational collapse and expansion solutions in Rastall theory of gravity. The field equations have been formulated for the non-static and inhomogeneous gravitating source. The Misner–Sharp mass function, auxiliary solution and trapped condition have been used to obtained a trapped surface. The auxiliary solutions have been used to obtain the expansion and collapse solutions; these solutions depend on $C (r, t)$ $C (r, t)$ and parameter $β$ $β$ (which appears due to parametric form of metric components); also the range of parameter $β$ $β$ has been examined. The expansion scalar $Θ$ $Θ$ depends on parameter $β$ $β$ , in the case of expansion $Θ > 0$ $Θ > 0$ for $β > - 2$ $β > - 2$ , while for collapse $Θ < 0$ $Θ < 0$ with $β < - 2$ $β < - 2$ . Also, the dynamics of the gravitating spherical source has been discussed graphically with the effects of Rastall parameter $λ$ $λ$ . For the physically reasonable fluid, the validity of energy conditions has been discussed for expansion and collapse solutions with the various values of $λ$ $λ$ .

Keywords:

PACS: 04.20.Cv, 04.20.Dw

References

1. S. W. Hawking and G. F. R. Ellis , The Large Scale Structure of Space Time (Cambridge University Press, 2011). Google Scholar
2. S. Hawking and R. Penrose , The Nature of Space and Time (Princeton University Press, USA, 1996). Crossref, Google Scholar
3. R. Penrose , Riv. Nuovo Cim. 1 (1969) 252. Google Scholar
4. P. S. Joshi and I. H. Dwivedi , Comun. Math. Phys. 146 (1992) 333342. Google Scholar
5. J. R. Oppenheimer and H. Snyder , Phys. Rev. 56 (1939) 455. Crossref, Google Scholar
6. J. T. Wheeler , Nucl. Phys. B 268 (1986) 737. Crossref, Web of Science, Google Scholar
7. K. Boshkayev, A. Idrissov, O. Luongo and D. Malafarina , MNRAS 496 (2020) 1115. Crossref, Web of Science, Google Scholar
8. S. Capozziello, R. D’Agostino and O. Luongo , Int. J. Mod. Phys. D 28 (2019) 1930016. Link, Web of Science, Google Scholar
9. O. Luongo and M. Muccino , Phys. Rev. D 98 (2018) 103520. Crossref, Web of Science, Google Scholar
10. I. Antoniadis, J. Rizos and K. Tamvakis , Nucl. Phys. B 415 (1994) 497. Crossref, Web of Science, Google Scholar
11. P. Kanti, J. Rizos and K. Tamvakis , Phys. Rev. D 59 (1999) 083512. Crossref, Web of Science, Google Scholar
12. L. Herrera, G. Le Denmat and N. O. Santos , Gen. Relativ. Gravit. 44 (2012) 1143. Crossref, Web of Science, Google Scholar
13. V. A. Skripkin , Sov. Phys. Dokl. 135 (1960) 1183. Google Scholar
14. E. N. Glass , Gen. Relativ. Gravit. 45 (2013) 266. Crossref, Web of Science, Google Scholar
15. G. Abbas and M. Tahir , Adv. High Energy Phys. 2018 (2018) 7420546. Google Scholar
16. M. Sharif and A. Saddiqa , Adv. High Energy Phys. 2019 (2019) 8702795. Google Scholar
17. G. Abbas and R. Ahmad , Eur. Phys. J. C 77 (2017) 441. Crossref, Web of Science, Google Scholar
18. C. Barceló, S. Liberati, S. Soneg and M. Visser , Phys. Rev. D 77 (2008) 044032. Crossref, Web of Science, Google Scholar
19. L. Herrera and N. O. Santos , Phys. Rep. 286 (1997) 53. Crossref, Web of Science, Google Scholar
20. L. Herrera, N. O. Santos and G. Le Denmat , MNRAS 237 (1989) 257. Crossref, Web of Science, Google Scholar
21. L. Herrera, J. Ospino and A. Di Prisco , Phys. Rev. D 77 (2008) 027502. Crossref, Web of Science, Google Scholar
22. S. Chakrabarti and N. Banerjee , Gen. Relativ Gravit. 57 (2016) 48. Google Scholar
23. D. G. Boulware and S. Deser , Phy. Rev. Lett. 55 (1985) 2665. Google Scholar
24. F. Tangherlini , Nuovo Cimento 27 (1963) 636. Crossref, Web of Science, Google Scholar
25. R. C. Myers and M. J. Perry , Ann. Phys. 172 (1986) 304. Crossref, Web of Science, Google Scholar
26. H. Maeda , Phy. Rev. D 73 (2006) 104004. Crossref, Web of Science, Google Scholar
27. S. Jhingan and S. G. Ghosh , Phys. Rev. D 81 (2010) 024010. Crossref, Web of Science, Google Scholar
28. C. W. Misner and D. Sharp , Phys. Rev. B 136 (1964) 571. Crossref, Web of Science, Google Scholar
29. C. W. Misner and D. Sharp , Phys. Rev. B 137 (1965) 1360. Crossref, Web of Science, Google Scholar
30. L. Herrera, A. Di Prisco and J. R Hernan Dezand, N. O. Santo , Phys. Lett. A 237 (1998) 113. Crossref, Web of Science, Google Scholar
31. L. Herrera and N. O. Santos , Phys. Rev. D 70 (2004) 084004. Crossref, Web of Science, Google Scholar
32. L. Herrera, A. Di Prisco and J. Ospino , Gen. Relativ. Gravit. 44 (2012) 2645. Crossref, Web of Science, Google Scholar
33. L. Herrera , Int. J. Mod. Phys. D 15 (2006) 2197. Link, Web of Science, Google Scholar
34. L. Herrera, N. O. Santos and A. Wang , Phys. Rev. D 78 (2008) 084024. Crossref, Web of Science, Google Scholar
35. G. Abbas , Sci. China. Phys. Mech. Astro. 57 (2014) 604. Crossref, Web of Science, Google Scholar
36. S. M. Shah and G. Abbas , Eur. Phys. J. C 77 (2017) 251. Crossref, Web of Science, Google Scholar
37. G. Abbas , Astrophys. Space Sci. 350 (2014) 307. Crossref, Web of Science, Google Scholar
38. G. Abbas , Adv. High Energy Phys. 2014 (2014) 306256. Crossref, Web of Science, Google Scholar
39. G. Abbas , Astrophys. Space Sci. 352 (2014) 955. Crossref, Web of Science, Google Scholar
40. G. Abbas and U. Sabiullah , Astrophys. Space Sci. 352 (2014) 769. Crossref, Web of Science, Google Scholar
41. S. Nojiri and S. D. Odintsov , Phys. Lett. B 599 (2004) 137. Crossref, Web of Science, Google Scholar
42. G. Allemandi, A. Borowiec, M. Francaviglia and S. D. Odintsov , Phys. Rev. D 72 (2005) 063505. Crossref, Web of Science, Google Scholar
43. P. Rastall , Phys. Rev. D 6 (1972) 3357. Crossref, Web of Science, Google Scholar
44. H. A. Ziaie and Y. Tavakoli, arXiv:1912.08890 [qr-qc]. Google Scholar
45. M. Visser , Phys. Lett. B 782 (2018) 83. Crossref, Web of Science, Google Scholar
46. F. Darabi, H. Moradpour, I. Licata, Y. Heydarzade and C. Corda , Eur. Phys. J. C 78 (2018) 25–28. Crossref, Web of Science, Google Scholar
47. S. Hansraj, A. Banerjee and P. Channuie , Ann. Phys. 400 (2019) 320–345. Crossref, Web of Science, Google Scholar
48. S. Hansraj and A. Banerjee, Mod. Phys. Lett. A, https://doi.org/10.1142/S0217732320501059. Google Scholar
49. H. Moradpour, A. Bonilla, E. M. C. Abreu and J. A. Neto , Phys. Rev. D 96 (2017) 123504. Crossref, Web of Science, Google Scholar
50. L. L. Smalley , J. Phys. A Math. Gen. 16 (1983) 2179–2185. Crossref, Google Scholar
51. G. Abbas and M. R. Shahzad , Astrophys. Space Sci. 363 (2018) 251–258. Crossref, Web of Science, Google Scholar
52. G. Abbas and M. R. Shahzad , Eur. Phys. J. A 54 (2018) 211–221. Crossref, Web of Science, Google Scholar
53. G. Abbas and M. R. Shahzad , Astrophys. Space Sci. 364 (2019) 50–61. Crossref, Web of Science, Google Scholar
54. G. Abbas and M. R. Shahzad , Chin. J. Phys. 63 (2020) 1–12. Crossref, Web of Science, Google Scholar
55. M. R. Shahzad and G. Abbas , Int. J. Geom. Meth. Mod. Phys. 9 (2019) 1950132. Link, Web of Science, Google Scholar
56. M. R. Shahzad and G. Abbas , Eur. Phys. J. Plus 135 (2020) 502. Crossref, Web of Science, Google Scholar
57. M. R. Shahzad and G. Abbas , Astrophys. Space Sci. 365 (2020) 147. Crossref, Web of Science, Google Scholar
58. J. C. Fabris, O. F. Piattella, D. C. Rodrigues, C. E. M. Batista and M. H. Daouda , Int. J. Mod. Phys. Conf. Ser. 18 (2012) 67–76. Link, Google Scholar
59. J. P. Campos, J. C. Fabris, R. Perez, O. F. Piattella and H. Velten , Eur. Phys. J. C 73 (2013) 2357. Crossref, Web of Science, Google Scholar
60. J. C. Fabris, M. H. Daouda and O. P. Piattella , Phys. Lett. B 711 (2012) 232. Crossref, Web of Science, Google Scholar
61. H. Moradpour , Phys. Lett. B 757 (2016) 187. Crossref, Web of Science, Google Scholar
62. A. S. Al-Rawaf and M. O. Taha , Gen. Relativ. Gravit. 28 (1996) 935. Crossref, Web of Science, Google Scholar
63. C. E. M. Batista, M. H. Daouda, J. C. Fabris, O. F. Piattella and D. C. Rodrigues , Phys. Rev. D 85 (2012) 084008. Crossref, Web of Science, Google Scholar
64. T. R. P. Carames, M. H. Daouda, J. C. Fabris, A. M. Oliveira, O. F. Piattella and V. Strokov , Eur. Phys. J. C 74 (2014) 3145. Crossref, Web of Science, Google Scholar
65. I. G. Salako, M. J. S. Houndjo and A. Jawad , Int. J. Mod. Phys. D 25 (2016) 1650076. Link, Web of Science, Google Scholar
66. L. L. Smalley , Phys. Rev. D 9 (1974) 1635. Crossref, Web of Science, Google Scholar
67. L. l. Smalley , Phys. Rev. D 12 (1975) 376. Crossref, Web of Science, Google Scholar
68. C. Wolf , Phys. Scr. 34 (1986) 193. Crossref, Web of Science, Google Scholar
69. H. Moradpour, Y. Heydarzade, F. Darabi and I. G. Salako , Eur. Phys. J. C 77 (2017) 259. Crossref, Web of Science, Google Scholar
70. R. Saleem and J. Hassan , Phys. Dark Univ. 28 (2020) 100515. Crossref, Web of Science, Google Scholar
71. T. Manna, F. Rahaman and M. Mondal, Mod. Phys. Lett. A, https://doi.org/10.1142/S0217732320500340. Google Scholar
72. Y. Heydarzade and F. Darabi , Phys. Lett. B 771 (2017) 365–373. Crossref, Web of Science, Google Scholar
73. M. S. Ma and R. Zhao , Eur. Phys. J. C 77 (2017) 629–635. Crossref, Web of Science, Google Scholar
74. K. Lin and W. L. Qian , Chin. Phys. C 43(8) (2019) 083106. Crossref, Web of Science, Google Scholar
75. M. F. A. R. Sakti, A. Suroso and F. P. Zen , Ann. Phys. 413 (2020) 168062. Crossref, Web of Science, Google Scholar
76. Y. Heydarzade, H. Moradpour and F. Darabi , Can. J. Phys. 95 (2017) 1253–1256. Crossref, Web of Science, Google Scholar
77. Z. Xu, X. Hou, X. Gong and J. Wang , Eur. Phys. J. C 78 (2018) 513–524. Crossref, Web of Science, Google Scholar
78. I. P. Lobo, H. Moradpour, J. P. Morais Graça and I. G. Salako , Int. J. Mod. Phys. D 27 (2018) 1–17. Link, Web of Science, Google Scholar
79. H. Moradpour, N. Sadeghnezhad and S. H. Hendi , Can. J. Phys. 95 (2017) 1257–1266. Crossref, Web of Science, Google Scholar
80. J. Liang , Commun. Theor. Phys. 70 (2018) 695–704. Crossref, Web of Science, Google Scholar
81. R. Kumar and S. G. Ghosh , Eur. Phys. J. C 78 (2018) 750–762. Crossref, Web of Science, Google Scholar
82. P. Lobo, H. Moradpour, J. P. Morais Graça and I. G. Salako , Int. J. Mod. Phys. D 27(7) (2018) 1850069. Link, Web of Science, Google Scholar
83. H. Moradpour and I. G. Salako , Adv. High Energy Phys. 2016 (2016) 3492796. Crossref, Web of Science, Google Scholar
84. K. Bamba, A. Jawad, S. Rafique and H. Moradpour , Eur. Phys. J. C 78 (2018) 986. Crossref, Web of Science, Google Scholar
85. A. H. Ziaie, H. Moradpour and S. Ghaffari , Phys. Lett. B 276 (2019) 793. Google Scholar
86. A. H. Ziaie and Y. Tavakoli, arXiv:1912.08890 [gr-qc]. Google Scholar