  This paper discusses the problem of gravitational perturbations of radiating
spacetimes. We lay out the theoretical framework for describing the interaction
of external gravitational fields with a radiating spacetime. This is done by
deriving the field perturbation equations for a radiating metric. The equations
are then specialized to a Vaidya spacetime. For the Hiscock ansatz of a linear
mass model of a radiating blackhole the equations are found separable. Further,
the resulting ordinary differential equations are found to admit analytic
solutions. We obtain the solutions and discuss their characteristics.
