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This research investigates the nature of spacetime through the lens of brane viscosity and its implications for gravitational interactions.

May 22, 2026Open Access

Newton's Constant as Brane Viscosity: Spacetime as a Non-Newtonian Fluid, MOND as Shear-Thinning, and the T1/T2/T2* Hierarchy as the Burgers Constitutive Equa- tion of the Brane

Key Points

This research investigates the nature of spacetime through the lens of brane viscosity and its implications for gravitational interactions.
Identifies Newton's constant as compliance in a crystalline fluid model.
Analyzes the brane fluid's behavior under varying acceleration conditions.
Utilizes the Burgers model to describe the relaxation hierarchy in spacetime.
Demonstrates the effective gravitational viscosity diverges at low acceleration, similar to shear-thinning polymers.
Establishes a relationship between brane viscosity and the gravitational Reynolds threshold.
Provides new predictions based on the derived SPARC rotation curve equation of the brane fluid.

Abstract

Newton's constant G is identied as the compliance (inverse shear viscosity) of the brane fabric regarded as a crystalline uid. From Paper XVI, G = c4/τbrane, where τbrane is the brane tension; tension is a viscosity-like quantity for a 2D material, so G is literally how easily spacetime deforms under a shear load. The brane uid is Newtonian at high acceleration (a ≫a0) and non-Newtonian at low acceleration (a ≲a0), with a0 = cH0/2π acting as the gravitational Reynolds threshold separating laminar from non-Newtonian ow. MOND phenomenology is the Carreau-Yasuda shear-thinning limit of this uid: the eective gravitational viscosity Geff(a) diverges as a →0 exactly as a shear-thinning polymer viscosity diverges at zero shear rate. The T1/T2/T2* relax- ation hierarchy (Papers XXXIV, XXXV) is identied as the three-component Burgers viscoelastic constitutive model: T1 is the Newtonian dashpot (global sump ow), T2 is the Kelvin-Voigt spring (stellar cluster elastic dephasing), and T2* is the Maxwell elas- tic element (coherent BH focal zone). The SPARC rotation curve equation from Paper XXXIV is derived as the constitutive equation of the brane uid, not postulated phe- nomenologically. Two dimensionless numbers complete the unication: the gravitational Weissenberg number Wigrav = (rT2∗/c)(a/a0) governs the elastic-to-viscous transition at xed radius, and the gravitational Deborah number Degrav = Tsump/tobs governs the quantum-mechanical (De ≫1, elastic) to MOND (De ≪1, viscous) transition across observation timescales. The G2-symmetric viscosity tensor has exactly two independent components in ratio 2πRbulk, restating the hierarchy problem as a viscosity ratio. The KSS bound η/s ≥ℏ/(4πkB) is saturated by the brane uid, which is the minimum- viscosity uid consistent with quantum mechanics a consequence of the Fano truss minimality. Four new predictions follow (Predictions 6568). Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.

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Bharathi Jagadeesan (Tue,) studied this question.

synapsesocial.com/papers/6a0ff496d674f7c03778db3f https://doi.org/https://doi.org/10.5281/zenodo.20299878

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