Reading off gravitational radiation waveforms in numerical relativity calculations: Matching to linearized gravity

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Abstract
Two methods are described, both based on the use of multipole moments in linearized gravity, to read off gravitational radiation waveforms during numerical relativity simulations. In the first, matching is made at a finite radius in the weak-field exterior of a strong-field source to an analytic template developed via an infinitesimal gauge transformation from a general solution to the vacuum weak-field equations. The matching procedure allows the asymptotic waveforms to be separated from the confusing influences of the source’s (e.g., black hole, neutron star, collapsing stellar core) stationary moments, the wave’s near-zone field, and gauge dependencies in the metric. This is achieved by computing the multipole-moment amplitudes of the gravitational field with a set of surface integrals of the metric over one (or more) coordinate two-sphere(s). The two-surface(s) need not be placed far out in the local wave zone, nor does the method require the existence of a deep near zone (i.e., the source need not be slow motion). The procedure is demonstrated through its application to two standard axisymmetric numerical relativity gauges (quasi-isotropic and radial). The second matching approach uses a surface integral over components of the Riemann tensor to eliminate gauge effects. The near-zone field is separated off as in the previous method. This latter technique may be applicable to problems in any gauge.