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, flat vacuum interior. Because anyonic degrees of freedom are naturally supported in an effective (2+1)-dimensional geometry, the shell behaves as a two-dimensional many-body system for which horizon area is the natural extensive variable. Its microstates are encoded in a finite constrained fusion Hilbert space, yielding a microscopic description of horizon degrees of freedom together with logarithmic and inverse-area corrections to the Bekenstein-Hawking entropy. An equipartition argument on the shell recovers the Hawking temperature at leading order and motivates a collective Hamiltonian whose constrained Gaussian fluctuations reproduce both the leading term and the logarithmic correction in the canonical entropy. Matching the microscopic, thermodynamic, and canonical entropy descriptions fixes the effective quantum dimension in closed form and points to candidate underlying anyon theories. Quantum information is stored nonlocally in the condensate's fusion channels, providing a finite horizon Hilbert space without invoking bulk trans-horizon entanglement. To address formation, we embed the shell in conformal gravity as an effective high-curvature framework and show that it admits a local, nonsingular matching between a regular flat interior and a Schwarzschild-like exterior. Phenomenologically, the timelike shell can support late-time gravitational-wave echoes if it is weakly reflective, while remaining compatible with standard surface-emission constraints provided infalling energy is absorbed without prompt thermal reradiation. Overall, this framework gives a concrete microscopic account of black hole thermodynamics grounded in topological quantum computation.