[Paper Review] Black Hole-Inspired Horizon Model for Neural Signal Dynamics

E. Canessa|arXiv (Cornell University)|Mar 16, 2026

Neural dynamics and brain function0 citations

TL;DR

The paper proposes a horizon-inspired framework where EEG observables are boundary projections of deeper neural dynamics, modeled as RG-driven wave-like modes parameterized by spectral entropy, with audible sonifications.

ABSTRACT

Electroencephalographic (EEG) signals provide macroscopic observables of complex neural dynamics. We introduce a horizon-inspired framework in which measured EEG signals are modeled as projections of a complex wave-like representation constrained by an effective boundary analogous to an event horizon. In this formulation the signal amplitude obeys a renormalization-group scaling relation while EEG spectral entropy parameterizes the accessibility of observable modes. The resulting solutions generate oscillatory structures whose geometry and spectral signatures can be explored through signal analysis and sonification. This mapping between entropy-based neural observables and wave-like signal representations provides a physically motivated framework linking entropy measures, scale-dependent dynamics, and observable neural oscillations, and suggests testable connections between spectral entropy and the amplitude scaling of EEG modes.

Motivation & Objective

• Motivate a physics-inspired, boundary-based description of EEG signals as projections of deeper neural dynamics.
• Introduce a renormalization-group (RG) structure governing the amplitude of neural wave modes.
• Connect EEG spectral entropy to the accessibility of observable neural modes via a horizon-like boundary.
• Provide a mathematical formulation that yields observable oscillatory patterns and sonified representations.
• Suggest testable predictions linking entropy, amplitude scaling, and neural state transitions.

Proposed method

• Define a complex neural activity wavefunction psi(r) with RG evolution: r d|psi|/dr = beta1|psi| + beta3|psi|^3 + ... .
• Derive the probability density rho(r)=|psi|^2 and the normalized wavefunction amplitude |psi(r)| ~ sqrt(beta/(Gamma_r)) with Gamma_r = 1 - rs/r.
• Introduce a horizon-like boundary rs and an accessibility parameter Gamma_r that links internal dynamics to observables.
• Relate entropy to horizon physics via S* = (rs/Lp)^2 = [ (r/Lp)(1 - Gamma_r) ]^2 and interpret spectral entropy Seeg as Re[Schwarzschild-like entropy].
• Express the observable real waveform Re[psi(t)] = sqrt(beta/Gamma_r) cos(omega t + beta beta2 ln|t/ t0 - 1|^beta2 + phi1).
• Propose sonification of the wavefunction to render neural dynamics as audible trajectories and spectrograms.

Experimental results

Research questions

• RQ1 How does spectral entropy influence the amplitude and spectral structure of observable EEG-like oscillatory modes within the horizon framework?
• RQ2 Can variations in the accessibility parameter Gamma_r capture neural state transitions (e.g., sleep stages) in terms of changes in amplitude scaling and phase?
• RQ3 What are the characteristic trajectories (linear, helical, double-helix) of the complex wavefunction and their EEG projections under different parameter regimes?
• RQ4 Do the model's predictions about entropy–horizon relations produce testable correlations in large EEG datasets?

Key findings

• The RG equation yields scale-invariant, fixed-point-like amplitude behavior for large r (r >> rs).
• Higher spectral entropy corresponds to a larger number of accessible neural configurations and a larger effective distance from the horizon boundary.
• A logarithmic phase modulation near the horizon emerges, yielding log-periodic oscillatory structure.
• The real part of the wavefunction provides audible waveforms suitable for sonification, linking physics-inspired parameters to EEG-like signals.
• Observable signals depend on Gamma_r and ω, enabling spectrogram structures that reflect entropy-controlled dynamics.
• The framework offers falsifiable predictions: entropy variations should modulate amplitude and spectral structure; lack of such correlation would falsify the model.