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

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.