An Efficient Numerical Method for Computing Gravitational Waves Induced by a Particle Moving on Eccentric Inclined Orbits around a Kerr Black Hole

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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 l-, k- and n-modes, where l 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 l 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).

Journal

  • Progress of Theoretical Physics

    Progress of Theoretical Physics 121(4), 843-874, 2009-04-25

    Published for the Yukawa Institute for Theoretical Physics and the Physical Society of Japan

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Codes

  • NII Article ID (NAID)
    110007339364
  • NII NACSIS-CAT ID (NCID)
    AA00791455
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    0033068X
  • NDL Article ID
    10214722
  • NDL Source Classification
    ZM35(科学技術--物理学)
  • NDL Call No.
    Z53-A468
  • Data Source
    CJP  NDL  NII-ELS 
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