A measure of complexity for axial self-gravitating static fluids

Abstract

One of the feasible potential candidates for illustrating the accelerating expansion of the cosmos can be taken through the notion of modified gravity. Within the context of metric f(R) gravity, the contribution of this work features a better understanding of complexity factors for anisotropic static fluid composition in axially symmetric spacetime. This is a generalization of the work done by Herrera et al (2019, Phys. Rev. D 99, 044 049). We formulate generalized dynamical and field equations for anisotropic sources in our analysis. We will compute three distinct complexity factors (Y TF1, Y TF2, Y TF3) after incorporating structure scalars via orthogonal breakdown of the curvature tensor. The differential equations for the conformal tensor are assessed in terms of these complexity factors for the physical illustration. It is inferred that all these factors vanish for the matter spheroid provided with energy homogeneity and isotropic pressure. Nonetheless, the vanishing of these factors might be observed in different scenarios. This happened because energy inhomogeneity and pressure anisotropy cancel out each other in the description of complexity factors. Certain exact solutions of this nature have been reported and studied. All of the outcomes would reduce to general relativity within usual limits.