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

TL;DR

The work proposes that black holes host a two-dimensional condensate of non-Abelian anyons localized on a thin shell just outside the horizon, with the interior remaining a regular constant-curvature vacuum. Horizon entropy and radiation emerge from the constrained fusion Hilbert space of the anyons and a discretized area spectrum, yielding S(A) = (A/4) minus logarithmic and inverse-area corrections, and a discrete mass spectrum M_n = \mu\sqrt{n} that produces thermally weighted, information-carrying transitions with T(M) approaching the Hawking form at leading order. A minimal, local formation mechanism within conformal gravity ensures a nonsingular interior and a consistent shell–exterior matching, and the model predicts potential late-time gravitational-wave echoes if the shell is reflective. The framework connects horizon microphysics to topological quantum computation ideas, providing a finite microscopic Hilbert space for horizon degrees of freedom and offering testable phenomenological signatures beyond standard bulk entanglement pictures.

Abstract

We model black holes as condensates of non-Abelian anyons forming a thin, topologically ordered, timelike shell located just outside the would-be horizon, while the interior settles into a regular, effectively empty constant-curvature vacuum. The horizon degrees of freedom are described by a finite, constrained fusion Hilbert space whose dimension, together with a quantized area spectrum, reproduces the Bekenstein-Hawking entropy and yields logarithmic and inverse-area corrections. To characterize the shell's thermodynamics, we introduce an effective collective Hamiltonian with global constraint modes; fluctuations of these constrained modes generate a logarithmic entropy correction that is consistent with the corrections obtained from area quantization. Combining the fusion-state degeneracy with the discrete area spectrum leads to a nonuniform, discrete black-hole mass spectrum and a corresponding thermally weighted emission profile. The Hawking temperature is recovered at leading order from classical equipartition on the shell, with systematic corrections controlled by the discrete spectrum. Quantum information is stored nonlocally in the fusion channels of the condensate, providing a finite microscopic Hilbert space for horizon degrees of freedom without explicitly invoking bulk trans-horizon entanglement. To address formation and consistency, we embed the shell in conformal gravity, used as an effective classical framework in the high-curvature regime, and construct a local, nonsingular matching between the regular interior, the shell, and a Schwarzschild-like exterior. The framework implies microscopic spectral discreteness and, for weak shell reflectivity, the possibility of late-time gravitational-wave echoes. Overall, our results provide a concrete microscopic model for black-hole thermodynamics and connect horizon microphysics to ideas from topological quantum computation.