Galileons and strong gravity
  In the context of a cubic Galileon model in which the Vainshtein mechanism
suppresses the scalar field interactions with matter, we study low-density
stars with slow rotation and static relativistic stars. We develop an expansion
scheme to find approximated solutions inside the Vainshtein radius, and show
that deviations from General Relativity (GR), while considering rotation, are
also suppressed by the Vainshtein mechanism. In a quadratic coupling model, in
which the scalarisation effect can significantly enhance deviations from GR in
normal scalar tensor gravity, the Galileon term successfully suppresses the
large deviations away from GR. Moreover, using a realistic equation of state,
we construct solutions for a relativistic star, and show that deviations from
GR are more suppressed for higher density objects. However, we found that the
scalar field solution ceases to exist above a critical density, which roughly
corresponds to the maximum mass of a neutron star. This indicates that, for a
compact object described by a polytropic equation of state, the configuration
that would collapse into a black hole cannot support a non-trivial scalar
field.
