Structure of compact stars: A pure geometric approach

This paper uses pure geometric field theory to construct a stellar model for a static spherically symmetric anisotropic compact star. The expression pure geometry means that all physical quantities and fields are defined in terms of the geometric objects of the geometry used. This implies the possibility of defining the material-energy tensor geometrically, not phenomenologically, from the geometry under consideration, absolute parallelism (AP-) geometry. Two solutions are obtained for the field equations of the theory, an interior solution and an exterior solution. The stellar model is obtained as an analytical solution of the field equations within the material distribution. An equation of state for anisotropic material distribution is derived from the model rather than being imposed on it. The vacuum solution of the field equations coincides with the Schwarzschild exterior solution. Matching the interior and exterior solutions at the boundary of the stellar configuration enables fixing the integration constants. The physical acceptability and stability analysis of the model are discussed, and the results show that the present model is suitable for studying the envelope region of a neutron star in a core-envelope type model. The model is investigated graphically using the estimated data of the pulsar 4U1820-30 with mass $1.58M_{\odot }$ and radius 9.1 km. In conclusion, this study demonstrates the feasibility of constructing a pure geometric stellar model and highlights the benefits of using such an approach to understand stellar structure.