  Multigravity theories are constructed from the discretization of the extra
dimension of five dimensional gravity. Using an ADM decomposition, the
discretization is performed while maintaining the four dimensional
diffeomorphism invariance on each site. We relate the Goldstone bosons used to
realize nonlinearly general covariance in discretized gravity to the shift
fields of the higher dimensional metric. We investigate the scalar excitations
of the resulting theory and show the absence of ghosts and massive modes; this
is due to a local symmetry inherited from the reparametrization invariance
along the fifth dimension.
