CURVATURE-BASED GAUGE-INVARIANT PERTURBATION-THEORY FOR GRAVITY - A NEW PARADIGM - ART. NO. 064015

A new approach to gravitational gauge-invariant perturbation theory be gins from the fourth-order Einstein-Ricci system, a hyperbolic formula tion of gravity for arbitrary lapse and shift whose centerpiece is a w ave equation for curvature. In the Minkowski and Schwarzschild backgro unds, an intertwining operator procedure is used to separate physical gauge-invariant curvature perturbations from unphysical ones. In the S chwarzschild case, physical variables are found which satisfy the Regg e-Wheeler equation in both odd and even parity. In both cases, the unp hysical ''gauge'' degrees of freedom are identified with violations of the linearized Hamiltonian and momentum constraints, and they are fou nd to evolve among themselves as a closed subsystem. If the constraint s are violated, say by numerical finite differencing, this system desc ribes the hyperbolic evolution of the constraint violation. It is argu ed that an underlying raison d'etre of causal hyperbolic formulations is to make the evolution of constraint violations well posed. [S0556-2 821(98)00518-9].