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Analytical high-order post-Newtonian expansions for spinning extreme mass ratio binaries

Chris Kavanagh1, Adrian C. Ottewill1, and Barry Wardell1,2

  • 1School of Mathematics and Statistics and Complex & Adaptive Systems Laboratory, University College Dublin, Belfield, Dublin 4, Ireland
  • 2Department of Astronomy, Cornell University, Ithaca, New York 14853, USA

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Phys. Rev. D 93, 124038 – Published 15 June, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.124038

Abstract

We present an analytic computation of Detweiler’s redshift invariant for a point mass in a circular orbit around a Kerr black hole, giving results up to 8.5 post-Newtonian order while making no assumptions on the magnitude of the spin of the black hole. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi, and employs a rigorous mode-sum regularization prescription based on the Detweiler-Whiting singular-regular decomposition. The approximations used in our approach are minimal; we use the standard self-force expansion to linear order in the mass ratio, and the standard post-Newtonian expansion in the separation of the binary. A key advantage of this approach is that it produces expressions that include contributions at all orders in the spin of the Kerr black hole. While this work applies the method to the specific case of Detweiler’s redshift invariant, it can be readily extended to other gauge-invariant quantities and to higher post-Newtonian orders.

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Phys. Rev. D 93, 124038– Published 15 June, 2016
  • Received 29 January 2016
Article part of CHORUS

© 2016 American Physical Society

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