Self-accelerating Massive Gravity: Hidden Constraints and
  Characteristics
  Self-accelerating backgrounds in massive gravity provide an arena to explore
the Cauchy problem for derivatively coupled fields that obey complex
constraints which reduce the phase space degrees of freedom. We present here an
algorithm based on the Kronecker form of a matrix pencil that finds all hidden
constraints, for example those associated with derivatives of the equations of
motion, and characteristic curves for any 1+1 dimensional system of linear
partial differential equations. With the Regge-Wheeler-Zerilli decomposition of
metric perturbations into angular momentum and parity states, this technique
applies to fully 3+1 dimensional perturbations of massive gravity around any
isotropic self-accelerating background. Five spin modes of the massive graviton
propagate once the constraints are imposed: two spin-2 modes with luminal
characteristics present in the massless theory as well as two spin-1 modes and
one spin-0 mode. Although the new modes all possess the same - typically
spacelike - characteristic curves, the spin-1 modes are parabolic while the
spin-0 modes are hyperbolic. The joint system, which remains coupled by
non-derivative terms, cannot be solved as a simple Cauchy problem from a single
non-characteristic surface. We also illustrate the generality of the algorithm
with other cases where derivative constraints reduce the number of propagating
degrees of freedom or order of the equations.
