  A new approach to gravitational gauge-invariant perturbation theory begins
from the fourth-order Einstein-Ricci system, a hyperbolic formulation of
gravity for arbitrary lapse and shift whose centerpiece is a wave equation for
curvature. In the Minkowski and Schwarzschild backgrounds, an intertwining
operator procedure is used to separate physical gauge-invariant curvature
perturbations from unphysical ones. In the Schwarzschild case, physical
variables are found which satisfy the Regge-Wheeler equation in both odd and
even parity. In both cases, the unphysical "gauge'' degrees of freedom are
identified with violations of the linearized Hamiltonian and momentum
constraints, and they are found to evolve among themselves as a closed
subsystem. If the constraints are violated, say by numerical
finite-differencing, this system describes the hyperbolic evolution of the
constraint violation. It is argued that an underlying raison d'\^etre of causal
hyperbolic formulations is to make the evolution of constraint violations
well-posed.
