Study on physical properties and characteristics of an anisotropic compact star model using Karmarkar Condition in ℱ(𝒬) gravity

The main aim of this study is to examine the behavior of physical parameters of an anisotropic compact star model demonstrating spherical symmetry in [Formula: see text] modified gravity. To evaluate the behavior and the stability of an anisotropic compact star model, we utilize the measured mass and radius of an anisotropic compact star model. This study obtained an anisotropic compact star model by solving Einstein’s field equations. The field equations have been simplified by an appropriate selection of the metric element [Formula: see text] and the Karmarkar condition. We solve field equation to develop a differential equation that establishes a relationship between two essential components of spacetime, namely [Formula: see text] and [Formula: see text]. A physical analysis of this model reveals that the resulting stellar structure for anisotropic matter distribution is a physically plausible representation of a compact star with an energy density of order [Formula: see text]. Using the Tolman–Oppenheimer–Volkoff equation, causality condition and Harrison–Zeldovich–Novikov Condition, we investigate the hydrostatic equilibrium and stability of the compact star Cen X-3. We further determined the mass–radius relation of this compact star for different values of [Formula: see text].