  We consider full perturbations to a covariantly defined Schwarzschild
spacetime. By constructing complex quantities, we derive two decoupled,
covariant and gauge-invariant, wave-like equations for spin-weighted scalars.
These arise naturally from the Bianchi identities and comprise a covariant
representation of the Bardeen-Press equations for scalars with spin-weight
$\pm2$. Furthermore, the covariant and gauge-invariant 1+1+2 formalism is
employed, and consequently, the physical interpretation of the energy-momentum
perturbations is transparent. They are written explicitly in terms of the
energy-momentum specified on spacelike three-slices. Ultimately, a Cauchy
problem is constructed whereby, an initial three-slice may be perturbed by an
energy-momentum source, which induces resultant gravitational fields.
