Topological Stabilization of Horizonless Compact Objects in the Divine Wave Model

Topological Stabilization of Horizonless Compact Objects in the Divine Wave Model (DWM) This paper develops a concrete stabilization mechanism for horizonless, Kerr-like compact objects using two structural ingredients already native to DWM: (i) an admissibility field Γ with a nondegenerate double-well potential supporting finite-thickness domain walls (thin-shell limit), and (ii) a compact phase sector Φ ∈ S^1 carried by a complex order parameter, yielding an integer-valued conserved winding charge n_top. Modeling the interface as a thin shell separating two admissibility phases, the effective radial energy contains wall tension, a vacuum-energy asymmetry term, and a topological stiffness contribution ~ C n_top^2 / R. For sufficiently large conserved charge, the resulting effective potential admits a stable equilibrium radius R_* with V''(R_*) > 0. A critical charge n_crit separates collapsing configurations from stabilized near-horizon configurations, providing a TOV-like threshold for horizon avoidance. Near threshold, the interface can reside at R_* = r_+(1+ε) with ε