Newtonian fractional-dimension gravity and the external field effect

Abstract

We expand our analysis of Newtonian Fractional-Dimension Gravity (NFDG), an extension of the classical laws of Newtonian gravity to lower dimensional spaces, including those with fractional (i.e., non-integer) dimension. We apply our model to four rotationally supported galaxies (NGC 5033, NGC 6674, NGC 5055, NGC 1090), in addition to other three galaxies (NGC 7814, NGC 6503, NGC 3741) which were analyzed in previous studies. NFDG is able to fit the rotation curves of all these galaxies without any dark matter component. We also investigate the possible violation of the strong equivalence principle, in relation to the External Field Effect (EFE), i.e., the dependence of the internal motion of a self-gravitating system under freefall on an external gravitational field. This effect is not present in Newtonian or Einstein gravity, but is predicted by some alternative theories of gravity. On the contrary, we show that NFDG does not imply the EFE, at least for values of the fractional dimension in the range $1 \leq D \leq 3$. Using improved NFDG numerical computations, we analyze the rotation curves of the aforementioned galaxies and obtain perfect fits to the experimental data, by using a fractional-dimension function $D\left (R\right )$ which characterizes each individual galaxy. In the galactic sample studied here with NFDG methods, we do not detect any significant differences between galaxies that are supposed to show/not show the EFE according to other alternative theories. A larger sample of galaxies will be needed to fully determine the absence of any external field effect in NFDG.