“Kludge” gravitational waveforms for a test-body orbiting a Kerr black hole

One of the most exciting potential sources of gravitational waves for low-frequency, space-based gravitational wave (GW) detectors such as the proposed Laser Interferometer Space Antenna (LISA) is the inspiral of compact objects into massive black holes in the centers of galaxies. The detection of waves from such ``extreme mass ratio inspiral'' systems (EMRIs) and extraction of information from those waves require template waveforms. The systems' extreme mass ratio means that their waveforms can be determined accurately using black hole perturbation theory. Such calculations are computationally very expensive. There is a pressing need for families of approximate waveforms that may be generated cheaply and quickly but which still capture the main features of true waveforms. In this paper, we introduce a family of such kludge waveforms and describe ways to generate them. Different kinds of kludges have already been used to scope out data analysis issues for LISA. The models we study here are based on computing a particle's inspiral trajectory in Boyer-Lindquist coordinates, and subsequent identification of these coordinates with flat-space spherical polar coordinates. A gravitational waveform may then be computed from the multipole moments of the trajectory in these coordinates, using well-known solutions of the linearised gravitational perturbation equations in flat space time. We compute waveforms using a standard slow-motion quadrupole formula, a quadrupole/octupole formula, and a fast-motion, weak-field formula originally developed by Press. We assess these approximations by comparing to accurate waveforms obtained by solving the Teukolsky equation in the adiabatic limit (neglecting GW backreaction). We find that the kludge waveforms do extremely well at approximating the true gravitational waveform, having overlaps with the Teukolsky waveforms of 95% or higher over most of the parameter space for which comparisons can currently be made. Indeed, we find these kludges to be of such high quality (despite their ease of calculation) that it is possible they may play some role in the final search of LISA data for EMRIs.