Addressing the missing matter problem in galaxies through a new fundamental gravitational radius

Abstract

We demonstrate that the existence of a Noether symmetry in $f(R)$ theories of\ngravity gives rise to a further gravitational radius, besides the standard\nSchwarzschild one, determining the dynamics at galactic scales. By this\nfeature, it is possible to explain the baryonic Tully-Fisher relation and the\nrotation curve of gas-rich galaxies without the dark matter hypothesis.\n