Geometric Modification of Neutron Star Tidal Deformability in the Zhang Effective Metric

The detection of gravitational waves from the binary neutron star merger GW170817 has provided stringent constraints on the tidal deformability of neutron stars. In this paper, we investigate how the internal S³ orientation field modifies the tidal deformability within the rotational-order geometric unification framework. Using the Zhang Effective Metric, we show that the geometric pressure alters the hydrostatic equilibrium and the effective equation of state (EOS) inside the star. We derive the modified Love number k₂ and the tidal deformability Λ for a canonical 1.4 M_☉ neutron star. We find that the geometric correction can shift Λ₁.₄ within the observational bounds set by GW170817, while providing a distinct geometric signature for future gravitational-wave detectors such as the Einstein Telescope.