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

By Stanislav Babak, Hua Fang, Jonathan R. Gair, K. Glampedakis, S. Hughes. 2006

135 citations recorded by the source corpus.

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 BoyerLindquist 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 spacetime. 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.

View Paper: https://www.semanticscholar.org/paper/940bfdfa67ad64f02b052e6ca4372d2346fd5849

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Citations in the corpus

Black hole perturbation theory and gravitational self-force (2021, methodology): “In lieu of accurate evolving waveforms, the development of data analysis methods has so far been based on “kludge” waveforms constructed using a host of additional approximations (primarily, post-Newtonian approximations for the fluxes) [77, 7, 71, 5, 181, 37].”
Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion (2008, methodology): “Use of post-Newtonian methods: Approximate waveforms which are qualitatively similar to real waveforms can be obtained using post-Newtonian methods or using hybrid schemes containing some post-Newtonian elements [26, 31, 32].”
Physics, Astrophysics and Cosmology with Gravitational Waves (2009, background): “The emitted gravitational radiation [317, 179, 178, 67, 171, 57] would consist of a very long wave train that carries information about the nearly geodesic trajectory of the test body, thereby providing a very clean probe to survey the spacetime geometry of the central object (which could be a Kerr ”