Cotton gravity and 84 galaxy rotation curves

Recently, as a generalization of general relativity, gravity theory has been proposed in which gravitational field equations are described by the Cotton tensor. That allows an additional contribution to potential point mass that rises linearly with radius $\Phi = -GM/r + \gamma r/2$, where $G$ is Newton constant. The coefficients $M$ and $\gamma$ constants integration should be determined individually for each physical system. When applied galaxies, coefficient $\gamma$, dimension acceleration, galaxy. This same having determine If small enough, linear term negligible at short distances, but can become significant large distances. In fact, it may contribute extragalactic systems. this paper, we derive effective equation applicable We then use numerically compute sample 84 rotating galaxies. galaxies span wide range, from stellar disk-dominated spirals gas-dominated dwarf do not assume radial density profile disk, bulge, or gas; only observed data. find rotation curves explained distribution baryons. due flexibility allow constant context gravity, "dark matter" some sense automatically included curvature spacetime. Consequently, even have assumed dominated dark matter need matter.