  The recent observations of neutron star mergers have changed our perspective
on scalar- tensor theories of gravity, favouring models where gravitational
waves travel at the speed of light. In this work we consider a scalar-tensor
set-up with such a property, belonging to a beyond Horndeski system, and we
numerically investigate the physics of locally asymptotically flat black holes
and relativistic stars. We first determine regular black hole solutions
equipped with horizons: they are characterized by a deficit angle at infinity,
and by large contributions of the scalar to the geometry in the near horizon
region. We then study configurations of incompressible relativistic stars. We
show that their compactness can be much higher than stars with the same energy
density in General Relativity, and the scalar field profile imposes stringent
constraints on the star properties. These results can suggest new ways to probe
the efficiency of screening mechanisms in strong gravity regimes, and can help
to build specific observational tests for scalar-tensor gravity models with
unit speed for gravitational waves.
