• Record: found
  • Abstract: found
  • Article: found
Is Open Access

Spherical harmonic modes of 5.5 post-Newtonian gravitational wave polarizations and associated factorized resummed waveforms for a particle in circular orbit around a Schwarzschild black hol


Read this article at

      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.


      Recent breakthroughs in numerical relativity enable one to examine the validity of the post-Newtonian expansion in the late stages of inspiral. For the comparison between post-Newtonian (PN) expansion and numerical simulations, the waveforms in terms of the spin-weighted spherical harmonics are more useful than the plus and cross polarizations, which are used for data analysis of gravitational waves. Factorized resummed waveforms achieve better agreement with numerical results than the conventional Taylor expanded post-Newtonian waveforms. In this paper, we revisit the post-Newtonian expansion of gravitational waves for a test-particle of mass \(\m\) in circular orbit of radius \(r_0\) around a Schwarzschild black hole of mass \(M\) and derive the spherical harmonic components associated with the gravitational wave polarizations up to order \(v^{11}\) beyond Newtonian. Using the more accurate \(h_{\ell m}\)'s computed in this work, we provide the more complete set of associated \(\rho_{\ell m}\)'s and \(\delta_{\ell m}\)'s that form important bricks in the factorized resummation of waveforms with potential applications for the construction of further improved waveforms for prototypical compact binary sources in the future. We also provide ready-to-use expressions of the 5.5PN gravitational waves polarizations \(h_+\) and \(h_\times\) in the test-particle limit for gravitational wave data analysis applications. Additionally, we provide closed analytical expressions for 2.5PN \(h_{\ell m}\), 2PN \(\rho_{\ell m}\) and 3PN \(\delta_{\ell m}\), for general multipolar orders \(\ell\) and \(m\) in the test-particle limit. Finally, we also examine the implications of the present analysis for compact binary sources in Laser Interferometer Space Antenna.

      Related collections

      Author and article information

      13 May 2010
      1005.2266 10.1103/PhysRevD.82.044051

      Custom metadata
      42 pages, 2 figures, match with accepted version by PRD


      Comment on this article