An efficient numerical method for computing gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole

Fujita, Ryuichi; Hikida, Wataru; Tagoshi, H.

Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/3824

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DC Field	Value	Language
dc.contributor.author	Fujita, Ryuichi	-
dc.contributor.author	Hikida, Wataru	-
dc.contributor.author	Tagoshi, H.	-
dc.date.accessioned	2009-07-31T11:09:15Z	-
dc.date.available	2009-07-31T11:09:15Z	-
dc.date.issued	2009-04	-
dc.identifier.citation	Progress of Theoretical Physics, 2009, Vol. 121, p843	en
dc.identifier.issn	0033-068X	-
dc.identifier.issn	1347-4081 (online)	-
dc.identifier.uri	http://hdl.handle.net/2289/3824	-
dc.description	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)	en
dc.description.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 stress-energy 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 n-modes, where \ell is the index of the spin-weighted 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 10-5 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).	en
dc.language.iso	en	en
dc.publisher	Progress of Theoretical Physics	en
dc.relation.uri	http://arxiv.org/abs/0904.3810	en
dc.relation.uri	http://dx.doi.org/10.1143/PTP.121.843	en
dc.relation.uri	http://adsabs.harvard.edu/abs/2009PThPh.121..843F	en
dc.rights	2009 Progress of Theoretical Physics	en
dc.title	An efficient numerical method for computing gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole	en
dc.type	Article	en
Appears in Collections:	Research Papers (TP)

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