Are Galactic Rotation Curves Really Flat?

Abstract

In this paper we identify an apparently previously unappreciated regularity in the systematics of galactic rotation curves; namely, we find that at the last detected points in galaxies of widely varying luminosity, the centripetal acceleration is found to have the completely universal form (v²/c²R)_last = γ₀/2 + γ*N*/2 + β*N*/R², where γ₀ and γ* are new universal constants, β* is the Schwarzschild radius of the Sun, and N* is the total amount of visible matter in each galaxy. This regularity points to a possible role for the linear potentials associated with conformal gravity, with the galaxy-independent γ₀ term being found not to be generated from within individual galaxies at all but rather to be of cosmological origin, being due to the global Hubble flow of a necessarily spatially open universe of 3-space scalar curvature k = -(γ₀/2)² = -2.3 × 10^-60 cm^-2.