Galactic Spacetime Solutions with a Varying Newton's Coupling

TL;DR

This paper introduces a new family of galactic spacetime solutions with a spatially varying Newton's coupling, explaining flat rotation curves and predicting a slight reduction in light deflection compared to Einstein's theory.

Contribution

It presents novel vacuum solutions with a varying Newton's coupling that account for galactic rotation curves without dark matter, highlighting geometric mass contributions.

Findings

Effective geometric mass receives negative non-baryonic contribution

Light deflection is slightly less than Einsteinian prediction

Solutions are observationally similar to dark matter models

Abstract

We find a new family of galactic metrics corresponding to flat rotation curves at the outer radii. These are vacuum solutions to a gravity theory where the Newton's coupling varies mildly in space. The effective `mass', whose origin is purely geometric, receives a negative non-baryonic contribution. The angle of deflection of a light ray propagating in this geometry is found to be diminished rather than enhanced compared to the Einsteinian bending, the effect being highly suppressed though. Hence, these spacetimes are observationally dintinguishable from other geometric or `dark matter' based alternatives invoked to explain mass discrepancies in galaxies.