Published January 22, 2026 | Version v1
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The Dark Halo as a Lattice Artifact: Deriving the Tully-Fisher Relation from Vacuum Elastodynamics

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Abstract

The empirical sterility of direct Dark Matter searches compels a radical ontological shift from particulate halos to Vacuum Rheology. Within the Holographic Information Tension (HIT) framework, the "Dark Halo" is reified not as hidden mass, but as a manifestation of Vacuum Elastodynamics intrinsic to a "World Crystal" substrate.

This paper posits that the entangled vacuum lattice exhibits non-Newtonian strain-hardening in the regime of vanishing curvature ($g \ll a_0$) and saturates the holographic Kovtun-Son-Starinets (KSS) viscosity bound. This rheological framework provides a unified solution to galactic kinematics and cosmological tensions without invoking exotic particles.

Key Derivations & Mechanisms:

  • The Baryonic Tully-Fisher Relation: The $M_b \propto v_{flat}^4$ scaling law is analytically deduced from the vacuum's stress response, identifying the acceleration scale $a_0$ as the fundamental yield stress gradient of the spacetime medium.
  • Resolution of the Hubble & S8 Tensions: The irreducible viscosity of the vacuum ($\eta_{vac}$) introduces a "cosmic friction," generating a dissipative redshift component that resolves the $H_0$ discrepancy and suppresses structure growth to match weak lensing data.
  • Gravitational Hysteresis: The anomalous lensing of the Bullet Cluster is explained via the rheological memory of the substrate (Viscoelastic Hysteresis), where the strain field fails to relax synchronously with the baryonic load during high-velocity mergers.

Falsifiable Predictions:

The crystalline ontology mandates specific, quantifiable deviations from General Relativity. We predict a fundamental Thermodynamic Hiss—a $1/f$ strain noise floor ($h_c \sim 10^{-16}$ at 1 Hz)—distinguishable from instrumental noise in next-generation atom interferometers (MAGIS-100, AION), alongside Post-Ringdown Echoes in black hole mergers.

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References

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