Tidal Love numbers, Deformability, and Universal Relations of an Analytic Gravastar-like Compact Object Model

We present a complete calculation of the quadrupolar tidal Love number k 2 and the associated tidal deformability Λ for a gravastar-like (Imran-class) analytic horizonless compact object with a regular interior matched to an exterior Schwarzschild spacetime. Building on our earlier static and slowly rotating analyses, we obtain the relativistic tidal response by integrating the Hinderer-Damour-Nagar tidal-perturbation equation on the exact background solution. From this, we construct the Λ-M and Λ-C relations, the k 2 -Λ correlation, and the full I-Love-Q-Λ relations for the model family. We find that the tidal response is strongly suppressed as the compactness approaches its maximum admissible value: k 2 and Λ decrease rapidly toward the Schwarzschild black-hole limit Λ BH = 0 while the configurations remain horizonless, whereas lower-compactness solutions have much larger deformabilities, comparable to ordinary compact stars. We compare these predictions with neutron star universal curves, the Kerr black hole reference point, NICER mass-radius measurements, and LIGO/Virgo tidal constraints from GW170817, outlining how current and future observations can test this gravastar-like framework.