Flatness in disc galaxy dynamics without MOND or dark matter

In previous work (astro-ph/0306228) we have established that a particular quasi-classical theoretical viewpoint about the nature of gravitation in galaxy discs provides extremely high concordance (comparable with MOND) with the observed dynamics in optical discs. In this paper, we consider the possibility that the optical disc and the flat radio disc represent distinct dynamical regions which are inherently described by distinct phases of the same over-arching theory of which the quasi-classical theory is but one phase. This is a defining moment for the theory under discussion since the only natural generalization available is that from the existing quasi-classical (one-clock) model into a quasi-relativistic (two-clock) model. The quasi-relativistic disc turns out to be a stationary hyperbolic disc within which information propagates along characteristics and within which the rotation curve is necessarily exactly flat. The transition between the two components of the disc is managed by physically determined jump conditions which are represented by a set of non-linear algebraic equations. These equations predict the existence of a forbidden region within the parameter space which coincides exactly with that part of the parameter space in which there is an already observed highly significant underpopulation of galaxy discs (astro-ph/0107300).