  We investigate strong coupling effects in a covariant massive gravity model,
which is a candidate for a ghost free non-linear completion of Fierz-Pauli. We
analyse the conditions to recover general relativity via Vainshtein mechanism
in the weak field limit, and find three main cases depending on the choice of
parameters. In the first case, the potential is such that all non-linearities
disappear and the vDVZ discontinuity cannot be avoided. In the second case, the
Vainshtein mechanism allows to recover general relativity within a macroscopic
radius from a source. In the last case, the strong coupling of the scalar
graviton completely shields the massless graviton, and weakens gravity when
approaching the source. In the second part of the paper, we explore new exact
vacuum solutions, that asymptote de Sitter or anti de Sitter space depending on
the parameter choice. The curvature of the space is proportional to the mass of
the graviton, thus providing a cosmological background which may explain the
present day acceleration in terms of the graviton mass. Moreover, by expressing
the potential for non-linear massive gravity in a convenient form, we also
suggest possible connections with a higher dimensional framework.
