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 << 1, where r_+ is the Kerr outer horizon radius and ε is controlled by microphysics and proximity to n_crit.

Because the exterior is Kerr-like for r ≳ R_*, leading-order lensing and early ringdown are approximately degenerate with classical black holes, while near-horizon boundary conditions modify late-time response. The model predicts gravitational-wave echoes with delay Δt_echo ~ κ_BH^{-1} ln(1/ε) and a frequency-domain comb with spacing Δf_echo ~ 1/Δt_echo. The ratio f_QNM / Δf_echo is mass-independent and depends only on ε and spin, providing a falsifiable discriminator. The framework also naturally allows dissipation channels (e.g., vortex-core losses and coupling to wall/phase excitations), mitigating the standard ergoregion-instability objection to perfectly reflecting rotating horizonless models.

Context / companion DWM records:
- The Divine Wave Model: An Operator-First Physical Framework (Zenodo: 18508094)
- Divine Wave Model Research Program (Executive Overview + Companion Papers) (Zenodo: 18461919)
- Astrophysical Consequences of Interface-Dominated Structure Formation (Zenodo: 18508831)

Keywords and references are provided in the accompanying BibTeX file (refs.bib).