The Bright Side of Dark Matter

TL;DR

The paper demonstrates that dark matter is essential for explaining galactic observations within a four-dimensional metric framework, as alternative models fail to produce correct gravitational lensing effects.

Contribution

It proves that without dark matter, constructing a four-dimensional metric consistent with galactic rotation curves and light bending is impossible.

Findings

Dark matter is necessary for correct gravitational lensing predictions.

Alternative metric models without dark matter produce repulsive light bending.

Dark matter preserves the validity of the equivalence principle at galactic scales.

Abstract

We show that it is not possible in the absence of dark matter to construct a four-dimensional metric that explains galactic observations. In particular, by working with an effective potential it is shown that a metric which is constructed to fit flat rotation curves in spiral galaxies leads to the wrong sign for the bending of light i.e. repulsion instead of attraction. Hence, without dark matter the motion of particles on galactic scales cannot be explained in terms of geodesic motion on a four- dimensional metric. This reveals a new bright side to dark matter: it is indispensable if we wish to retain the cherished equivalence principle.