Quantum Vortices as Black Hole Analogs in Logarithmic Superfluid Vacuum Theory

This paper develops a detailed theoretical correspondence between quantized vortices in a logarithmic superfluid vacuum and black holes in general relativity, advancing the superfluid vacuum theory (SVT) program initiated by Volovik, Zloshchastiev, and others. Within this framework, the physical vacuum is modeled as a Bose-Einstein condensate governed by the logarithmic nonlinear Schrödinger equation—a choice motivated by its unique property of yielding a density-independent speed of sound. This provides a natural mechanism for the observed constancy of the speed of light across different spacetime regions, a feature absent in polynomial nonlinearities. The central result establishes that black holes correspond to topological defects—quantum vortices where the superfluid order parameter vanishes, creating genuine "holes" in the emergent spacetime fabric. We derive the effective acoustic metric surrounding such vortices and demonstrate the emergence of ergosphere-like structures where the azimuthal flow velocity exceeds the sound speed. A systematic mapping is established between vortex parameters and black hole characteristics: winding number corresponds to angular momentum (suggesting fundamental quantization of black hole spin), vortex energy maps to gravitational mass, the healing length relates to the Planck scale, and the vortex core corresponds to the singularity. The phenomenological matching conditions required to connect superfluid parameters to observed gravitational constants are explicitly stated as matching conditions rather than first-principles derivations. The framework carries significant implications for early universe cosmology. If the universe underwent a phase transition to its current superfluid vacuum state, the Kibble-Zurek mechanism would generically produce a spectrum of vortex defects—corresponding to primordial black holes without requiring prior stellar evolution or special density fluctuations. This may offer new perspectives on recent JWST observations of anomalously massive black holes at high redshift. This work places black holes within the broader context of topological defects in quantum field theory and provides a foundation for investigating fundamental questions including singularity resolution, horizon area quantization, and the microscopic origin of Hawking radiation.