Mass-radius ratio bounds for compact objects in Lorentz-violating dRGT massive gravity theory

We consider the mass-radius bounds for spherically symmetric static compact objects in the de Rham-Gabadadze-Tolley (dRGT) massive gravity theories, free of ghosts. In this type of gravitational theories the graviton, the quantum of gravity, may have a small, but non-vanishing mass. We derive the hydrostatic equilibrium and mass continuity equations in the Lorentz-violating massive gravity in the presence of a cosmological constant and for a non-zero graviton mass. The case of the constant density stars is also investigated by numerically solving the equilibrium equations. The influence of the graviton mass on the global parameters (mass and radius) of these stellar configurations is also considered. The generalized Buchdahl relations, giving the upper and lower bounds of the mass-radius ratio are obtained, and discussed in detail. As an application of our results we obtain gravitational redshift bounds for compact stellar type objects in the Lorentz-violating dRGT massive gravity, which may (at least in principle) be used for observationally testing this theory in an astrophysical context.