NEWTONIAN FRACTIONAL-DIMENSION GRAVITY (NFDG)

Main Content

INTRODUCTION TO NFDG

NFDG is a new alternative model of gravity that I introduced in 2020, with three papers on the subjects (see links at the top of this page). The goal of NFDG is to model galactic rotation curves, without using the controversial Dark Matter (DM). This is done by assuming that galactic structures might behave as fractal media, with an effective dimension which can be lower than the standard value D = 3. This includes also possible fractional, i.e. non-integer, dimensions. This model is broadly based on the methods of fractional mechanics and fractional calculus, and is connected with Modified Newtonian Dynamics (MOND), a leading alternative theory of gravity introduced by M. Milgrom in 1983.

In the first paper (published version), I used NFDG to model several types of spherically-symmetric structures, while in the second paper (published version) I did the same for axially-symmetric structures. However, the real objective of NFDG is to model existing galactic rotation curves, obtained from the SPARC database or others. In the second paper, I produced the first NFDG example of detailed data fitting, for the disk-dominated galaxy NGC 6503 (see photo, NASA/ESA Hubble Space Telescope).

Below, I show the NFDG analysis of this galaxy: the top panel shows the variable dimension D as a function of the radial distance R, computed with NFDG models. This dimension is very close to a constant value D=2 over most of the radial range. Results for low-R values (below the gray vertical line) were extrapolated and are not completely reliable. Bottom panel: NFDG galactic rotation curves compared with SPARC data. There is perfect agreement between the main NFDG (SPARC) curve (green-solid) and the experimental data. This shows that, if this galaxy behaves as a fractal structure whose dimension D follows the green-solid curve in the top panel, the resulting NFDG circular velocity curve in the bottom panel (green-solid) will perfectly fit the experimental data, without any need of dark matter. See my second paper (published version) for full details.

In a third paper on the subject, I extended the NFDG anlysis to two additional galaxies: NGC 7814 and NGC 3741. See also the links at the bottom of this page with more detailed information.

NFDG analysis of NGC 6503. Top panel: variable space dimension D as a function of the radial distance R. Bottom panel: NFDG rotation curves (circular velocity vs. radial distance) compared to the original SPARC data.

NEW GALACTIC FITS

FUTURE WORK ON THE SUBJECT 

NGC  7814 

NGC 7814 bulge dominated spiral galaxy. It is located about 40 million light-years away, in the constellation Pegasus. The galaxy is seen edge-on from Earth and sometimes referred to as "the little sombrero". NFDG results for NGC 7814.  

NGC 3741 

NGC 3741 gas dominated spiral galaxy. It is an irregular galaxy in the constellation Ursa Major and was discovered by John Herschel in 1828. NFDG results for NGC 3741. 

FRACTIONAL DIMENSION 

The physical origin of the frational dimension will need to be studied, possibly arising from the fractal structure of galaxies and other astrophysical objects.

RFDG 

A relativistic version of NFDG - Relativistic Fractional-Dimension Gravity (RFDG) - will need to be introduced, by expanding standard General Relativity to metric spaces with fractional dimension.