Construction of Astrophysical Initial Data for Perturbations of Relativistic Stars

TL;DR

This paper presents a new method for constructing initial data for perturbations of relativistic stars, aiding simulations of gravitational waves from astrophysical sources like merging neutron stars.

Contribution

It introduces a conformal approach to generate initial data sets for perturbations around spherically symmetric matter distributions, linking them to standard gauge variables.

Findings

Framework successfully constructs initial data for relativistic star perturbations

Examples include initial data for merging neutron stars in close-limit approximation

Establishes correspondence between initial data and standard perturbation variables

Abstract

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.