Is dark matter a phantom ?

TL;DR

This paper proposes a novel solution to Einstein's equations in a non-standard gauge that explains galaxy rotation curves and dark matter phenomena without invoking new particles.

Contribution

It introduces a new vacuum solution with flat rotation curves and derives a matter density consistent with the Tully-Fisher relation.

Findings

Vacuum solutions exhibit asymptotically flat rotation curves.

Matter density aligns with the Tully-Fisher relation.

Model reproduces galaxy rotation dynamics without dark matter particles.

Abstract

We show that Einstein's equations in a non-standard gauge have vacuum solutions with an asymptotically flat rotation curve as it is observed in the dark halos of galaxies. Introducing a material disk into this model we find a matter density in accordance with the Tully-Fisher relation.