Equations of motion, in cylindrical co-ordinates, for the observed rotation of gases within the gravitational potential of spiral galaxies have been derived from Carmeli's Cosmological General Relativity theory. A Tully-Fisher type relation results and rotation curves are reproduced without the need for non-baryonic halo dark matter. Two acceleration regimes are discovered that are separated by a critical acceleration approximate to 4.75 x 10(-1)0 m s(-2). For accelerations larger than the critical value the Newtonian force law applies, but for accelerations less than the critical value the Carmelian regime applies. In the Newtonian regime the accelerations fall off as r(-2), but in the Carmelian regime the accelerations fall off as r(-1). This is new physics but is exactly what is suggested by Milgrom's phenomenological MOND theory.
Hartnett, J. (2006). Spiral Galaxy Rotation Curves Determined from Carmelian General Relativity. International Journal of Theoretical Physics, 45(11), 2147-2165. https://doi.org/10.1007/s10773-006-9178-0