Stability, energy conditions, and model viability of compact stars in f(R) gravity

In this paper, we study the stability of various compact stars (Formula: see text) by analyzing the matching conditions between the interior metric, characterized by the Krori–Barua coefficients, and the exterior Schwarzschild metric. We investigate anisotropic compact stars in modified gravity theory by examining two distinct Formula: see text models. We analyze key stability parameters, including energy density, radial and tangential pressures, and additional stability criteria. This analysis deepens our understanding of astrophysical compact objects and their gravitational dynamics. All these quantities must remain positive throughout the stellar interior, with a finite energy density at the center. We explicitly verify these conditions in our model and illustrate them graphically, demonstrating that the chosen Formula: see text configuration yields physically realistic and viable compact-star solutions under relevant cosmological settings. In addition, we conduct a detailed analysis of the energy conditions within the framework of Formula: see text gravity, the null energy condition (NEC), weak energy condition (WEC), strong energy condition (SEC), and dominant energy condition (DEC), for structural reliability of Formula: see text. The stability parameters may be beneficial in classifying feasible and realistic Formula: see text gravitational models across a range of important cosmological instances. In order to verify the correctness and applicability of the proposed approach, we lastly cross-reference our important results with both the observational data and earlier theoretical models, like the Starobinsky model.