Exploring the physics of relativistic compact stars: an anisotropic model with quadratic equation of state in buchdahl geometry

By using the quadratic equation of state and the anisotropic energy-momentum tensor for compact stars in spherically symmetric spacetime in hydrostatic static equilibrium to solve Einstein's field equation, we are able to create a new class of models for compact stars. We developed new solutions by solving the field equations for the distribution of matter using a well-known Buchdahl metric potential (Buchdahl in Phys. Rev. D 116:1027, 1959). The resulting anisotropic solutions exhibit good behavior and obey the energy conditions. By analyzing the TOV equation, we have confirmed the stability of the produced model, Harrison-Zeldovik-Novikov criterion, and the adiabatic index for the solution. The fulfillment of all these criteria makes this model to be utilized for the study of realistic compact objects. Also, we measured the masses and radii of star candidates like "4U 1820-30", "PSR J1903+327", "4U 1608-52", "Vela X-1", "PSR J1614-2230", and "Cyg X-2" through this model and found these values compatible with observational values of corresponding stars. For each of the considered compact stars, we have obtained the approximate value of the moment of inertia via the obtained solution.