Black Holes as Non-Abelian Anyon Condensates: Implications for the Information Paradox

Abstract

We propose a black-hole model in which the would-be horizon is replaced by a thin, topologically ordered timelike shell of condensed non-Abelian anyons surrounding a regular, topologically trivial vacuum interior. The transition is modeled as an effective bosonization of the underlying matter, producing a $(2+1)$-dimensional many-body phase in which area is the natural extensive variable. The shell microstates form a finite constrained fusion Hilbert space that reproduces the Bekenstein--Hawking entropy. The associated discrete area and mass spectra yield logarithmic and inverse-area thermodynamic corrections. Classical equipartition of coarse-grained shell modes recovers the Hawking temperature and motivates a quadratic collective Hamiltonian whose canonical entropy reproduces the leading and logarithmic terms. Matching these descriptions relates the collective mode number to the quantum dimension and points to candidate anyon theories. We use conformal gravity as an effective high-curvature description of the transition region. The condensate can persist as a Planck-thick ultraviolet remnant within a spacetime well described by Einstein gravity at larger scales. The conformal field equations admit local nonsingular matching between the vacuum interior and a Schwarzschild-like exterior, while the leading radial dynamics admit a conditionally stable near-horizon branch with a finite constitutive threshold, unlike the divergent near-horizon response of the corresponding Israel shell in general relativity. Information remains encoded nonlocally in fusion channels, allowing radiation through shell-state transitions without bulk trans-horizon entanglement or an independent holographic microscopic description. Strong absorption suppresses an equilibrium interior radiation bath and conventional surface-emission signatures, while residual reflectivity can generate gravitational-wave echoes.