  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.

General Relativity and Quantum Cosmology