Emergent Spacetime and Superfluid Black Holes

Addressing the persistent theoretical tensions within the standard ΛCDM cosmologicalmodel—specifically the Hubble constant (H0) discrepancy, the Core-Cusp problem on galactic scales,and the enigmatic nature of Dark Energy and Dark Matter—this study proposes a fundamental onto-logical reconstruction. We construct a rigorous theoretical framework that reinterprets the classicalspacetime manifold as an emergent superfluid vacuum, physically realized as a Bose-Einstein Con-densate (BEC) governed by the Logarithmic Schr¨odinger Equation (LogSE). The core contributionof this paper is the transformation of the intuitive analogy of “gaseous space (vacuum)” versus “watervortex (black hole)” into a precise hydrodynamic analytical solution under the LogSE. We demon-strate that this vacuum possesses a dual-phase structure: a homogeneous ground state (Phase A)which drives cosmic acceleration via negative pressure generated by logarithmic nonlinearity andexhibits non-zero bulk viscosity to alleviate the Hubble tension; and an inhomogeneous excited state(Phase B) which forms quantized vortices and solitons, manifesting as galactic dark matter halos. Byapplying the Madelung transformation, we derive the modified Euler equation containing the quan-tum potential, proving that quantum pressure naturally stabilizes galactic cores, thereby resolvingsmall-scale structural anomalies. Furthermore, utilizing linear perturbation theory, we derive the ef-fective acoustic metric within the condensate, demonstrating that regions of supersonic flow formacoustic event horizons isomorphic to those of general relativistic black holes. Finally, we confrontthis framework with multi-messenger astronomical observations from LHAASO and GW170817,arguing that Lorentz Invariance is an emergent symmetry of the superfluid low-energy sector, thussatisfying current stringent constraints on Lorentz Invariance Violation (LIV).