In a recent paper, Herrera (Phys Rev D 97: 044010, 2018) have proposed a new definition of complexity for static self-gravitating fluid in general relativity. In the present article, we implement this definition of complexity for static self-gravitating fluid to case of f (R) gravity. Here, we found that in the frame of f (R) gravity the definition of complexity proposed by Herrera, entirely based on the quantity known as complexity factor which appears in the orthogonal splitting of the curvature tensor. It has been observed that fluid spheres possessing homogenous energy density profile and isotropic pressure are capable to diminish their the complexity factor. We are interested to see the effects of f (R) term on complexity factor of the self-gravitating object. The gravitating source with inhomogeneous energy density and anisotropic pressure have maximum value of complexity. Further, such fluids may have zero complexity factor if the effects of inhomogeneity in energy density and anisotropic pressure cancel the effects of each other in the presence of f (R) dark source term. Also, we have found some interior exact solutions of modified f (R) field equations satisfying complexity criterium and some applications of this newly concept to the study of structure of compact objects are discussed in detail. It is interesting to note that previous results about the complexity for static self-gravitating fluid in general relativity can be recovered from our analysis if f (R) = R, which general relativistic limit of f (R) gravity.
In this outline we recognize the idea of complexity factor for static anisotropic selfgravitating source with generalized f (R) metric gravity theory. In present consideration, we express the Einstein field equations, hydrostatic equilibrium equation, the mass function and physical behavior of f (R) model by using some observational data of well known compact stars like 4U 1820 − 30, SAX J1808.4 − 3658 and Her X − 1. We define the scalar functions through the orthogonal splitting of the Reimann-Christofell tensor and then find the vanishing complexity condition for self-gravitating system with the help of these scalars. It has been found that the vanishing condition for the complexity are pressure anisotropy and energy density inhomogeneity must cancel each other. Moreover, we study the momentous results of an astral object for the vanishing of complexity factor. Finally, these solutions reduced to previous investigation about complexity factor in General Relativity by taking λ = 0.
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