Complexity Factor For Anisotropic Source in Non-minimal Coupling Metric $f(R)$ Gravity

Abstract

In this outline we recognize the idea of complexity factor for static anisotropic self-gravitating 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 $\lambda=0$.