# Galactic rotation curves in Einstein's conformal gravity

## TL;DR

This paper demonstrates that Einstein's conformal gravity, with a specific rescaled metric, can accurately explain galactic rotation curves for a large galaxy sample without invoking dark matter, using only two universal parameters.

## Contribution

It provides an exact solution within Einstein's conformal gravity that accounts for galactic rotation curves without dark matter, based on a Weyl conformally invariant metric.

## Key findings

- Successfully fits rotation curves of 104 galaxies
- Uses only two universal parameters derived from data
- Eliminates the need for dark matter in galactic dynamics

## Abstract

We show quantitatively that an exact solution of Einstein's conformal gravity can explain very well the galactic rotation curves for a sample of 104 galaxies without need for dark matter or other exotic modification of gravity. The metric is an overall rescaling of the Schwarzschild-de Sitter spacetime as required by Weyl conformal invariance, which has to be spontaneously broken, and the velocity of the stars depends only on two universal parameters determined on the base of the observational data.