Unimodular Relativity and the Dark Matter Problem

TL;DR

This paper proposes a modification to unimodular relativity that introduces an extra gravitational acceleration term, potentially explaining dark matter effects without requiring unseen matter.

Contribution

It introduces a new divergence law in unimodular relativity leading to a modified gravitational acceleration that accounts for dark matter phenomena.

Findings

The modified theory predicts an additional acceleration proportional to the gradient of mass density.

The weak-field limit analysis shows compatibility with observed astrophysical accelerations.

The approach offers an alternative explanation for dark matter effects within a modified gravity framework.

Abstract

We introduce a modified divergence law for the energy-momentum tensor in the theory of unimodular relativity. Consequently, an additional equation for the measure field follows from the divergence of the field equations. The equations of motion are derived and the weak-field, low-velocity limit is investigated. It is found that the gravitational acceleration acquires a term that is proportional to the gradient of the mass density. We show that this term can provide the additional acceleration observed on astrophysical scales without the need for dark matter.