An Analyticity Obstruction to Deep MOND in Regular Equilibrium Media: Implications for Yang–Mills Dipolar Dark Matter

Abstract

The deep-MOND constitutive relation is unusual from the viewpoint of an ordinary equilibrium medium. We show that any local, rotationally invariant response that is analytic in the gravitational field near zero acceleration has the form D(g) = g [χ₀ + χ₂|g|² + χ₄|g|⁴ + …] Consequently, after cancellation of the linear susceptibility, the leading regular response scales as D ∝ g³, whereas deep MOND requires D ∝ g². We formulate this mismatch as a nonanalyticity criterion: deep MOND cannot arise from a regular, local, isotropic, analytic equilibrium branch with no additional spatial order parameter. We apply the criterion to the recent Yang–Mills dipolar-dark-matter construction of Blanchet and Seraille and show that its MOND term evades the regular-equilibrium obstruction through coherent homogeneous modes whose amplitudes retain initial-condition information. Ordinary passive damping removes that memory only by damping the MOND-carrying modes themselves.