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Title:  An efficient numerical method for computing gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole 
Authors:  Fujita, Ryuichi Hikida, W. Tagoshi, H. 
Issue Date:  Apr2009 
Publisher:  Progress of Theoretical Physics 
Citation:  Progress of Theoretical Physics, 2009, Vol. 121, p843 
Abstract:  We develop a numerical code to compute gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole. For such systems, the black hole perturbation method is applicable. The gravitational waves can be evaluated by solving the Teukolsky equation with a point like source term, which is computed from the stressenergy tensor of a test particle moving on generic bound geodesic orbits. In our previous papers, we computed the homogeneous solutions of the Teukolsky equation using a formalism developed by Mano, Suzuki and Takasugi and showed that we could compute gravitational waves efficiently and very accurately in the case of circular orbits on the equatorial plane. Here, we apply this method to eccentric inclined orbits. The geodesics around a Kerr black hole have three constants of motion: energy, angular momentum and the Carter constant. We compute the rates of change of the Carter constant as well as those of energy and angular momentum. This is the first time that the rate of change of the Carter constant has been evaluated accurately. We also treat the case of highly eccentric orbits with e = 0.9. To confirm the accuracy of our codes, several tests are performed. We find that the accuracy is only limited by the truncation of \ell, k and nmodes, where \ell is the index of the spinweighted spheroidal harmonics, and n and k are the harmonics of the radial and polar motion, respectively. When we set the maximum of \ell to 20, we obtain a relative accuracy of 105 even in the highly eccentric case of e = 0.9. The accuracy is better for lower eccentricity. Our numerical code is expected to be useful for computing templates of the extreme mass ratio inspirals, which is one of the main targets of the Laser Interferometer Space Antenna (LISA). 
Description:  Restricted Access. An openaccess version is available at arXiv.org (one of the alternative locations) 
URI:  http://hdl.handle.net/2289/3824 
ISSN:  0033068X 13474081 (online) 
Alternative Location:  http://arxiv.org/abs/0904.3810 http://dx.doi.org/10.1143/PTP.121.843 http://adsabs.harvard.edu/abs/2009PThPh.121..843F 
Copyright:  2009 Progress of Theoretical Physics 
Appears in Collections:  Research Papers (TP)

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