Analytical solutions to Einstein field equations for spherically symmetric anisotropic matter: a comparative study using Tolman VII metric potential

Abstract In this paper, we present analytical solutions to the Einstein field equations for spherically symmetric anisotropic matter distributions using the well-established Tolman VII metric potential, chosen for its strong physical and mathematical foundations. Our solutions are derived using three distinct approaches: the vanishing complexity factor condition (VCC), the embedding class I condition (ECC), and the conformally flat condition (CFC). We conduct a comprehensive comparative analysis of these three approaches. By ensuring a smooth match between the interior spacetime metric and the exterior Schwarzschild metric, and applying the condition of vanishing radial pressure at the boundary, we determine the model parameters. We graphically assess the model’s stability by examining conditions such as causality, the adiabatic index, equations of state, and the generalized Tolman–Oppenheimer–Volkov (TOV) equation, considering the forces acting within the system. Additionally, the effects of anisotropy on the stars’ physical characteristics are investigated through graphical representations.