Dynamics of singularity-free anisotropic solutions for charged compact stars in general relativity

This study introduces two unique, singularity-free solutions for anisotropic spherical systems coupled with an electromagnetic field. We firstly derive the Einstein-Maxwell equations for a static spherically symmetric spacetime. The corresponding anisotropy is then introduced which we use to determine our solutions. To ensure physical validity of the proposed models, we outline several conditions whose fulfilment is essential. The field equations are solved under two constraints, such as varying forms of the radial metric function and the anisotropic pressure. These assumptions yield two second-order differential equations in terms of the temporal component whose solutions involve integration constants. We fix these constants by matching the interior metric and the Reissner-Nordström exterior spacetime at the boundary. We also impose vanishing radial pressure at the surface to determine these constants. Using observed masses and radii of six star pulsars, we analyze the proposed solutions graphically for different charge values. Both models satisfy all physical conditions, demonstrating that the anisotropic matter distributions accurately describe compact stars under the Einstein’s gravity theory.