  As is well known, both massive gravity and bigravity exhibit the linear van
Dam-Veltman-Zakharov (vDVZ) discontinuity that is cured classically by the
nonlinear Vainshtein mechanism due to certain low scale strongly coupled
interactions. Here we show how both the vDVZ and strong coupling problems can
be removed by embedding 4D covariant massive gravity into a certain 5D warped
geometry. The 4D theory is a nonlinear strongly coupled massive gravity, that
is being coupled to a 5D bulk theory that generates a bulk graviton mass via a
one loop diagram. This induced mass leads to an additional 4D kinetic term for
the 4D longitudinal mode, even on flat space. Due to this kinetic term the 4D
massive theory becomes weakly coupled all the way up to a high energy scale set
by the bulk cosmological constant. The same effect leads to a suppression of
the interactions of the 4D longitudinal mode with a 4D matter stress-tensor,
thus removing the vDVZ discontinuity. The proposed mechanism has a pure 4D
holographic interpretation: a 4D nonlinear massive gravity mixes to a
non-conserved symmetric tensor of a 4D CFT that has a cutoff; the latter mixing
generates a large kinetic term for the longitudinal mode, and this makes the
longitudinal mode be weakly coupled to a matter stress-tensor, and weakly
self-coupled, all the way up to the scale of the 4D CFT cutoff.
