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We consider the mass-radius bounds for spherically symmetric static compactobjects in the de Rham-Gabadadze-Tolley (dRGT) Massive Gravity theories, freeof ghosts. In this type of gravitational theories the graviton, the quantum ofgravity, may have a small, but non-vanishing mass. We derive the hydrostaticequilibrium and mass continuity equations in the Lorentz-violating Massivegravity in the presence of a cosmological constant and for a non-zero gravitonmass. The case of the constant density stars is also investigated bynumerically solving the equilibrium equations. The influence of the gravitonmass on the global parameters (mass and radius) of these stellar configurationsis also considered. The generalized Buchdahl relations, giving the upper andlower bounds of the mass-radius ratio are obtained, and discussed in detail. Asan application of our results we obtain gravitational redshift bounds forcompact stellar type objects in the Lorentz-violating dRGT Massive Gravity,which may (at least in principle) be used for observationally testing thistheory in an astrophysical context.

Mass - radius ratio bounds for compact objects in Lorentz-violating dRGT Massive Gravity theory