G(2) Glueball Boson Stars as Restricted Kerr Mimickers in the Thomas--Fermi Limit

Abstract

We investigate whether horizonless compact stars made of dark glueball matter from a broken exceptional $G(2)$ gauge sector can reproduce selected Kerr observables within a Thomas--Fermi effective-fluid description. We introduce GC9, a scale-separated $G(2)$-inspired positive nonic-density closure whose high-density stiffness, bag-free surface and Q-ball safety make it a useful compact-star benchmark. After Thomas--Fermi rescaling, reduced stellar observables are independent of the microscopic glueball mass $m_G$, while the collective stiffness $Λ_T$ fixes the dimensional mass and radius. Solving the TOV, Hinderer and Hartle--Thorne systems, we obtain a stable maximum-mass compactness $C=0.3247$, tidal deformability $Λ=4.37$, $\bar I C^{3/2}=0.947$, and slow-rotation quadrupole $\bar Q=1.522$. At $j=0.328$, the same-order ISCO shift is $1.24\%$. The stable endpoint has no light ring, but its exterior Regge--Wheeler barrier supports a genuine static axial mode, $Mω=0.463846-0.098881i$, with a damping time about ten percent shorter than Schwarzschild and a real frequency $24.1\%$ higher. A polarization-balanced vector realization has the same isotropic bulk EOS; moderate residual anisotropy changes static and first-order observables only at the few-percent level, while the full coupled vector spectrum remains open. Cowling calculations identify matter-supported quadrupolar modes. The scalar-burst, seeded-collapse and cosmological sections are phenomenological: a fixed $Λ_T$ gives a compact Kerr-comparison branch only near its own maximum mass, so the multi-sector scenario assumes distinct constant-$Λ_T$ branches from the keV supermassive sector to the PeV asteroid-mass sector. GC9 therefore defines a falsifiable restricted Kerr-mimicry framework for gravitational-wave, horizon-scale and compact-dark-matter tests.