On the spacetime of a galaxy

We present an exact solution of the averaged Einstein's field equations in the presence of two real scalar fields and a component of dust with spherical symmetry. We suggest that the spacetime found provides the characteristics required by a galactic model that could explain the supermassive central object and the dark matter halo at once, since one of the fields constitutes a central oscillaton surrounded by dust and the other scalar field distributes far from the coordinate centre and can be interpreted as a halo. We show the behaviour of the rotation curves all along the background. Thus the solution could be a first approximation of a 'long exposition photograph' of a galaxy.