  The Higgs mechanism at the graviton level formulated as a Vainshtein
mechanism in time domains implies that the extra-degrees of freedom become
relevant depending on the direction of time (frame of reference) with respect
to the preferred time direction (preferred frame) defined by the St\"uckelberg
function $T_0(r,t)$ which contains the information of the extra-degrees of
freedom of the theory. In this manuscript, I make the general definition of the
Higgs mechanism by analyzing the gauge symmetries of the action and the general
form of the vacuum solutions for the graviton field. In general, the symmetry
generators depending explicitly on the St\"uckelberg fields are broken at the
vacuum level. These broken generators, define the number of Nambu-Goldstone
bosons which will be eating up by the dynamical metric in order to become
massive.
