A unified analytical equation of state for compact stars: Bridging neutron stars and gravastars with the Imran-class model

We present the Imran-Class Gravastar (ICG), a novel analytical model for compact stellar objects that provides an exact, isotropic and horizonless solution to Einstein’s field equations. The model’s key innovation lies in its curvature-dependent geometric formulation, which generates a self-consistent quadratic equation of state [Formula: see text] directly from spacetime geometry, eliminating the dependence on empirical nuclear equations of state. This geometrically derived approach ensures automatic satisfaction of all energy conditions and causality requirements while maintaining dynamical stability ([Formula: see text]) throughout the stellar interior. The analytical framework produces closed-form expressions for mass, radius, and compactness, yielding maximum masses of [Formula: see text]–[Formula: see text] with radii [Formula: see text]–[Formula: see text], in agreement with modern observational constraints from NICER and gravitational-wave observations. Unlike traditional neutron star models, the ICG configuration exhibits systematically softer pressure profiles (5–15% reduction), lower compactness ([Formula: see text]), and reduced surface redshifts ([Formula: see text]), while preserving full dynamical stability against radial perturbations. The model predicts fundamental oscillation modes at [Formula: see text] [Formula: see text]kHz with well-defined overtone structures, placing these signatures within detectable ranges for current and next-generation gravitational-wave observatories and providing testable discriminants from conventional neutron stars. The ICG framework establishes a new theoretical bridge between conventional neutron stars and horizonless compact objects, offering a geometrically derived, fully analytical alternative to numerical equation-of-state approaches for strong-field gravity research.