Compact star models in Einstein–Cartan gravity: The Finch–Skea Ansatz with spin-density effects

This paper investigates compact star models within Einstein–Cartan theory, where space–time torsion is coupled to the intrinsic spin of matter. The Newman–Penrose–Jogia–Griffiths formalism is used to develop the field equations for a static, spherically symmetric space–time. By applying the Finch–Skea geometric ansatz and assuming a linear equation of state with a chosen spin-density profile, exact analytic solutions are obtained. The model is examined under standard physical requirements, such as positive and decreasing density and pressure, causality, and stability. The application of the model to the pulsar PSR J1614–2230 confirms that these conditions are satisfied. The analysis suggests that spin–torsion effects introduce a repulsive component that supports equilibrium, making Einstein–Cartan theory a consistent extension of general relativity for describing compact objects with intrinsic spin.