Dark matter in galaxies according to the tensor-four-scalars theory II

TL;DR

This paper explores vacuum solutions in a modified gravity theory to model dark matter halos with constant rotation curves, using a novel gauge and expressing the metric in terms of the rotation curve.

Contribution

It introduces a new approach to derive vacuum solutions with asymptotically constant rotation curves in the tensor-four-scalars theory, extending previous work on dark matter modeling.

Findings

Derived explicit vacuum solutions with flat rotation curves

Connected metric expressions directly to observed rotation curves

Proposed a new gauge method for solving modified gravity field equations

Abstract

We continue to study the spherically symmetric vacuum solutions of the tensor-four-scalars theory which is a modification of general relativity. Our aim is to construct vacuum solutions with asymptotically constant circular velocity curves which can be used to represent the dark halo outside the baryonic matter. These solutions are obtained by means of a new non-standard gauge in the field equations. The metric is expressed in terms of the rotation curve $V(r)$ in closed form.