Galaxy Rotation Curves from Superfluid Vacuum Theory: A Unified Framework with Vortex–Black Hole Correspondence

This paper presents a complete theoretical framework for galaxy rotation curves derived from Superfluid Vacuum Theory (SVT) based on the logarithmic nonlinear Schrödinger equation. We demonstrate that the isothermal equation of state P = bρ inherent to logarithmic quantum fluids produces a characteristic velocity profile V(r) ∝ √ln(1 + r/rₖ), yielding flat rotation curves without requiring dark matter particles. The "missing mass" is reinterpreted as gravitating rotational kinetic energy of quantized vacuum vortices nucleated by rotating baryonic matter.Testing against 175 galaxies from the SPARC database yields median χ²ᵥ = 2.53, statistically equivalent to the NFW dark matter halo model (χ²ᵥ = 2.37). In head-to-head comparison, SVT outperforms NFW in 50.9% of galaxies. The framework naturally explains the Baryonic Tully-Fisher Relation through an explicit mass-dependent factor and resolves the cusp-core problem via the soft logarithmic density profile. We provide complete fitting formulae and Python implementation for observational testing.