Gauge-invariant treatment of gravitational radiation near the source: Analysis and numerical simulations

We discuss a procedure based on the use of multipole-moment expansions for matching numerical solutions for the gravitational-radiation field around a compact source to linear analytic solutions. Gauge-invariant perturbation theory is used to generate even- and odd-parity matching equations for each spherical harmonic order $l$, $m$. This technique determines asymptotic wave forms, valid in the local wave zone, from the numerically evolved fields in a weak-field annular region surrounding the isolated source. The separation of the wave form from near-zone and residual gauge effects is demonstrated using fully general-relativistic simulations of relativistic stars undergoing nonradial pulsation.