Emergent Newtonian Gravity from the Collective Acoustic Metric of a Logarithmic Superfluid Vacuum
Year: 2026
Type: preprint
Abstract: A companion paper showed that the Painlevé–Gullstrand (PG) flow v = √(2GM/r) regularizes the static-metric pathology of the logarithmic superfluid vacuum, yielding the PPN parameter γ = 1 for any barotropic equation of state. This paper derives that macroscopic flow as a collective mean-field effect of N microscopic vortex-Gausson solitons — the topological defects of the logarithmic condensate. The self-consistency requirement selects the PG flow uniquely: the static solution fails catastrophically (the spatial-to-temporal metric ratio diverges at the background equation-of-state exponent α = −1), while the PG flow closes the self-consistency loop exactly. Postulating that each soliton sources the acoustic metric through a localized perturbation yields an emergent gravitational constant G_eff ∼ c²/(ξ²ρ₀), where ξ is the healing length and ρ₀ the vacuum condensate mass density — an expression independent of the source mass M and distance r. Matching G_eff to Newton's constant, together with the natural condensate packing density n₀ ∼ 1/ξ³, determines ξ ∼ ℓ_P (the Planck length) and ρ₀ ∼ m_P/ℓ_P³ (the Planck density). An independent derivation from the Bernoulli relation of the logarithmic fluid confirms that Newtonian gravity (δρ ∝ 1/r) requires exactly the PG velocity profile (v² ∝ 1/r). The continuity constraint linking these is discussed as an open problem.
Author: Kulangiev, Benny Boris
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162196514
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