Boson and neutron stars with increased density

We discuss boson stars and neutron stars, respectively, in a scalar-tensor gravity model with an explicitly
time-dependent real scalar field. While the boson stars in our model - in contrast to the neutron stars - do
not possess a hard core, we find that the qualitative effects of the formation of scalar hair are similar in both
cases : the presence of the gravity scalar allows both type of stars to exist for larger central density as well
as larger mass at given radius than their General Relativity counterparts. In particular, we find new types
of neutron stars with scalar hair which have radii very close to the corresponding Schwarzschild radius and
hence are comparable in density to black holes. This new branch of solutions is stable with respect to the
decay into individual baryons.