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Complexity factor for dynamical spherically symmetric fluid distributions in $f (R)$ gravity

H. Nazar

http://orcid.org/0000-0001-6570-7953

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

E-mail Address: hammadnazar350@gmail.com

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and

G. Abbas

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

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

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https://doi.org/10.1142/S0219887819501706Cited by:20 (Source: Crossref)

Abstract

In this study, we analyze the complexity factor that is extended up to the dynamical spherically symmetric non-static case with anisotropic dissipative self-gravitating fluid distribution in context of $f (R)$ theory of gravity. For this evaluation we choose the particular $f (R)$ model that signifies the physical nature of the self-gravitating system. The proposed work discusses not only the complexity factor of the structure of the fluid distribution, but also defines the minimization rate of complexity of the pattern of evolution. Here, first we have applied similar approach for obtaining the structure scalar $Y_{T F}$ of the complexity factor as used for in the static case, and next we have described explicitly the dissipative and non-dissipative cases by assuming the simplest pattern of evolution (homologous condition). It has been found that the system configuration fulfills the vanishing condition of complexity factor and emerging homologously, corresponds to a energy density homogeneity, shearfree and geodesic, isotropic in pressure. Moreover, we define the stability results for the vanishing complexity factor condition. Finally, we would like to mention that these results are satisfying the prior investigation about complexity factor in General Relativity (GR) by setting $β = 0$ .

Keywords:

AMSC: 83C05, 83C15, 85-XX

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