  We study the massive gravity theory proposed by Arkani-Hamed, Georgi and
Schwartz. In this theory, the graviton becomes massive when general covariance
is spontaneously broken through the introduction of a field that links two
metrics, one of the which will eventually decouple. The excitation of this
"link" field acts like a Goldstone boson in giving mass to the graviton. We
work out the graviton and Goldstone boson propagators explicitly by means of
gauge fixing terms similar to the renormalizability gauges used in gauge
theories. With these propagators, we calculate the lowest order tree-level
interaction between two external energy momentum tensors. The result is
independent of the gauge parameter, but different from the prediction of
massless gravity theory, i.e., general relativity. This difference remains even
if the mass of the graviton goes to zero, in which case it gives the van
Dam-Veltman-Zakharov (vDVZ) discontinuity between the propagators of a massive
and massless linearized graviton. Moreover, we show that the Fierz-Pauli
graviton mass term can be considered as the ``unitary gauge'' of a more general
theory with an extra scalar field. We explicitly construct such a theory in
which the vDVZ discontinuity arises with a graviton mass term that is different
from the Fierz-Pauli mass term. This theory has a local Weyl symmetry under
conformal transformations of the metric. In the case when the mass goes to
zero, the Weyl summetry becomes a global symmetry. It is possible that the
local Weyl symmetry will give a hint as to the form of the corresponding fully
nonlinear theory having a nonzero graviton mass.
