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Here I develop the simplest method in order to evaluate whether or not theVainshtein mechanism can operate for a given set of parameters in a givensolution. The method is based on the formulation of the mechanism in terms ofthe St\"uckelberg functions given in Int.J.Mod.Phys. D24 (2015) 1550022 andarXiv:1305.0475 [gr-qc]. In such a case, the Vainshtein scale appears as anextremal condition of the dynamical metric. If we fix the graviton mass, we candefine the effective Vainshtein scale. Then for parameters where the Vainshteinscale vanishes or becomes smaller than the gravitational radius, the mechanismshould be absent. At the other extreme, if the Vainshtein scale is finite orinfinite, then the mechanism can operate. For consistency, if we define theVainshtein scale as an invariant, then we should expect the effective gravitonmass to become very large when the Vainshtein mechanism operates. On the otherhand, if the mass scale tends to zero, then the extra-degrees of freedom arefree to propagate. For clarity, here I analyze the effective mass behavior forthe different type of modes.

The Vainshtein conditions: The Vainshtein mechanism in terms of St\"uckelberg functions