Construction of initial data for perturbations of relativistic stars

We develop a framework for constructing initial data sets for perturbations about spherically symmetric matter distributions. This framework facilitates setting initial data representing sources of gravitational radiation involving relativistic stars. The procedure is based on the Lichnerowicz-York 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.