An Einstein-like theory of gravity with a non-newtonian weak-field limit

TL;DR

This paper introduces a modified gravity model with a scalar field that produces a logarithmic gravitational potential at large distances, potentially explaining galaxy rotation curves without dark matter by sacrificing Einstein equivalence at galactic scales.

Contribution

It presents a new scalar-tensor gravity model with a non-Newtonian weak-field limit, offering an alternative explanation for galactic rotation curves.

Findings

Weak-field solutions exhibit a logarithmic potential at large distances

Newtonian gravity appears as a subleading term in the model

Potential to explain galaxy rotation curves without dark matter

Abstract

We propose a model describing Einstein gravity coupled to a scalar field with an exponential potential. We show that the weak-field limit of the model has static solutions given by a gravitational potential behaving for large distances as \ln r . The Newtonian term GM/r appears only as subleading. Our model can be used to give a phenomenological explanation of the rotation curves of the galaxies without postulating the presence of dark matter. This can be achieved only by giving up at galactic scales Einstein equivalence principle.