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The idea of this paper is to look some anisotropic star models in a metric approach, where R is the Ricci scalar. The Karmarkar and Tolman system is used to analyze the physics of some spherically symmetric stars using two independent computational gravitational theories. The behavior of structural factors is evaluated using diagrams, and the feasibility of compact objects is investigated using boundary conditions for the involved constants. The investigation in the profiles of the effective energy/matter states, the equilibrium phases, and the Tolman‐Oppenheimer‐Volkoff models and stability analysis is performed for various realistic candidates of stars. Under a few important cosmological backgrounds, the assessment of our graphics may offer assistance in the search of the realistic and viable gravitational models.

This work is devoted to the study of some dynamical features of spherical relativistic locally anisotropic stellar geometry in f(R) gravity. In this paper, a specific configuration of tanh f(R) cosmic model has been taken into account. The mass function through technique introduced by Misner–Sharp has been formulated and with the help of it, various fruitful relations are derived. After orthogonal decomposition of the Riemann tensor, the tanh modified structure scalars are calculated. The role of these tanh modified structure scalars (MSS) has been discussed through shear, expansion as well as Weyl scalar differential equations. The inhomogeneity factor has also been explored for the case of radiating viscous locally anisotropic spherical system and spherical dust cloud with and without constant Ricci scalar corrections.

The aim of this work is to analyze the role of shear evolution equation in the modeling of relativistic spheres in [Formula: see text] gravity. We assume that non-static diagonally symmetric geometry is coupled with dissipative anisotropic viscous fluid distributions in the presence of [Formula: see text] dark source terms. A specific distribution of [Formula: see text] cosmic model has been assumed and the spherical mass function through generic formula introduced by Misner-Sharp has been formulated. Some very important relations regarding Weyl scalar, matter variables and mass functions are being computed. After decomposing orthogonally the Riemann tensor, some scalar variables in the presence of [Formula: see text] extra degrees of freedom are calculated. The effects of the polynomial modified structure scalars in the modeling of through Weyl, shear, expansion scalar differential equations are investigated. The energy density irregularity factor has been calculated for both anisotropic radiating viscous with varying Ricci scalar and for dust cloud with present Ricci scalar corrections.