DETERMINING GRAVITATIONAL-RADIATION FROM NEWTONIAN SELF-GRAVITATING SYSTEMS

Quadrupole gravitational radiation formulae are tested and compared in a calculation of rotating stellar core collapse. While the standard quadrupole formula (SQF) allows an economical calculation of the waveform in postlinear gravity, it has several shortcomings that become apparent in a finite difference (FD) calculation. These shortcomings are related to the large-moment arm of the quadrupole moment and the two (numerical) time derivatives that separate it from the waveform. These shortcomings lead to high-frequency noise in the SQF waveform. Several alternatives to the SQF are developed. Each is mathematically equivalent to the SQF and applicable to self-gravitating sources. All are intended to reduce either the moment arm by which the source is sampled, the number of time derivatives that are required to determine the waveform, or both. We find that for FD calculations, the new quadrupole formulae are all superior to the SQF and capable of producing waveforms free of the high-frequency noise characteristic of its use.