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

## TL;DR

This paper proposes a new gravitational radius derived from Noether symmetry in $f(R)$ gravity theories, which can explain galactic rotation curves and the baryonic Tully-Fisher relation without dark matter.

## Contribution

It introduces a novel gravitational radius from $f(R)$ gravity symmetry, providing an alternative explanation for galactic dynamics.

## Key findings

- Derivation of a new gravitational radius from Noether symmetry.
- Explanation of galactic rotation curves without dark matter.
- Reproduction of the baryonic Tully-Fisher relation.

## Abstract

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