Static, spherically symmetric objects in type-II minimally modified gravity

Static, spherically symmetric solutions representing stars made of barotropic perfect fluid are studied in the context two theories type-II minimally modified gravity, VCDM and VCCDM. Both these share property that no additional degree freedom is introduced gravity sector, propagate only gravitational waves besides matter fields, as General Relativity (GR). We find that, on imposing physical boundary conditions Misner-Sharp mass system, V(C)CDM exactly coincide with ones GR; namely, they also satisfy Tolman-Oppenheimer-Volkoff equation.