Modeling anisotropic non-vacuum exterior spacetimes matched with the Tolman IV interior solution for compact stars

This study investigates a class of static, spherically symmetric non-vacuum exterior spacetimes intended to model the anisotropic matter distribution surrounding compact stars. The exterior geometry is constructed using a Schwarzschild-like metric ansatz with an additional power-law term of the form [Formula: see text], where [Formula: see text] and n are constants, allowing the effective description of exotic or repulsive gravitational effects, particularly for [Formula: see text]. Due to the adopted metric structure, the resulting spacetime belongs to a generalized Kiselev-type geometry, for which the effective radial pressure satisfies [Formula: see text] while anisotropy arises through the tangential pressure component. The energy density, radial pressure, and tangential pressure are obtained directly from the Einstein field equations and remain regular throughout the exterior region. To assess physical viability, the exterior solution is smoothly matched with the Tolman IV interior solution at the stellar boundary and applied to realistic compact star candidates such as Her[Formula: see text]X-1 and Cen[Formula: see text]X-3. A detailed numerical analysis involving density, pressures, anisotropy, energy conditions, mass–radius ratio, redshift, and stability criteria demonstrates that the model satisfies all regularity and matching requirements. The results indicate that this framework provides a consistent effective description of anisotropic compact-star exteriors embedded in dark-energy-like fields and may be useful for modeling stellar envelopes or non-vacuum exterior environments.