Gravitational Implications of Electromagnetic Charge 4D Spherically Anisotropic Spactime

In this study, we examine the behavior of an anisotropic fluid—one where pressures differ in radial and tangential directions—under the influence of gravity and electromagnetic charge in a four-dimensional, spherically symmetric spacetime. We consider both collapsing and expanding scenarios governed by Einsteins field equations, which describe how matter and energy affect the curvature of spacetime. To model a realistic astrophysical setting, we assume the interior of the spacetime is filled with the charged anisotropic fluid, while the exterior is described by the Reissner–Nordström metric, which represents the spacetime outside a charged, non-rotating mass. The two regions are smoothly joined using the Darmois matching conditions, ensuring that the geometry and physical quantities remain continuous at the boundary. Our analysis focuses on how the presence of electric charge and pressure anisotropy affects the dynamics of the fluid. Specifically, we investigate the profiles of energy density and pressure during both collapse and expansion. The results show that charge plays a significant role in influencing the fluids behavior, potentially resisting or enhancing the collapse depending on its magnitude. We also explore the evolution of anisotropy and demonstrate its impact through graphical analysis. The energy density, pressure, and anisotropy factor are plotted to visualize how they evolve in the presence of charge. These findings contribute to a deeper understanding of how anisotropic and charged fluids behave in dynamic gravitational settings, and they may have implications for astrophysical objects like charged compact stars or models of early-universe expansion.