  We develop a framework for constructing initial data sets for perturbations
about spherically symmetric matter distributions. This framework facilitates
setting initial data representing astrophysical sources of gravitational
radiation involving relativistic stars. The procedure is based on
Lichnerowicz-York's conformal approach to solve the constraints in Einstein's
equations. The correspondence of these initial data sets in terms of the
standard gauge perturbation variables in the Regge-Wheeler perturbation
variables is established, and examples of initial data sets of merging neutron
stars under the close-limit approximation are presented.
