Physical Viability of Relativistic Polytropes with Pressure Anisotropy and Electric Charge

This study introduces a new class of physically viable solutions to the Einstein-Maxwell field equations, based on the inclusion of a charged anisotropic fluid distribution within the framework of general relativity. This is achieved by using a generalized polytropic equation of state alongside a specific transformation designed to make the field equations more manageable. The system is closed by introducing a specific spacetime ansatz, which is necessary because the unknowns exceed the available equations. Several polytropic models are developed under different choices of the corresponding index, specifically η = 1,1/2,2/3. The interior and exterior solutions are also matched at the hypersurface to invoke the junction conditions. Afterwards, we explore the physical characteristics of these charged models graphically against the estimated data of a star Vela X-1 as a case study. Finally, the results show that our developed models satisfy all standard criteria for astrophysical viability, including hydrostatic equilibrium, causality, and the necessary stability conditions.