  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. 
Compact objects in scalar-tensor theories after GW170817