Fractional-Dimension Gravity and the Milky Way Galaxy

Abstract: In this work, we focus our analysis of Fractional-Dimension Gravity (FDG) on our home galaxy, the Milky Way (MW), by using the latest Gaia DR3 data as well as previous rotation curve (RC) data for this galaxy. FDG is an alternative gravitational model (previously known as Newtonian Fractional-Dimension Gravity - NFDG) which does not require the dark matter (DM) paradigm. The MW is studied here with the methods of FDG and its observed rotation curves are successfully reproduced by using a variable fractional dimension $D\left (R\right)$, following previous studies of several other galaxies which were analyzed with the same methodology. An alternative dimension function $D_{m}\left(R \right)$, based on the mass-dimension field equation, was also used and yielded less accurate fits to the experimental data. In addition, we also considered possible implications of the FDG metric, based on the presence of additional weights, on the structure of Special Relativity (SR) for spacetimes with fractional dimension. One notable outcome of this analysis is the possibility of an effective superluminal motion in galactic regions where the space dimension is $D<3$. Although this result is very speculative, it opens interesting new perspectives for possible interstellar travel in our galaxy.