Spin-dependent two-body interactions from gravitational self-force computations
Abstract
We analytically compute, through the eight-and-a-half post-Newtonian order and the fourth-order in spin, the gravitational self-force correction to Detweiler's gauge invariant redshift function for a small mass in circular orbit around a Kerr black hole. Using the first law of mechanics for black hole binaries with spin [L.~Blanchet, A.~Buonanno and A.~Le Tiec, Phys.\ Rev.\ D {\bf 87}, 024030 (2013)] we transcribe our results into a knowledge of various spin-dependent couplings, as encoded within the spinning effective-one-body model of T.~Damour and A.~Nagar [Phys.\ Rev.\ D {\bf 90}, 044018 (2014)]. We also compare our analytical results to the (corrected) numerical self-force results of A.~G.~Shah, J.~L.~Friedman and T.~S.~Keidl [Phys.\ Rev.\ D {\bf 86}, 084059 (2012)], from which we show how to directly extract physically relevant spin-dependent couplings.
Keywords
Cite
@article{arxiv.1510.06230,
title = {Spin-dependent two-body interactions from gravitational self-force computations},
author = {Donato Bini and Thibault Damour and Andrea Geralico},
journal= {arXiv preprint arXiv:1510.06230},
year = {2016}
}
Comments
19 pages, 5 figures, revtex macros used; misprints corrected in the 8.5PN-level coefficients of $-h_{kk}^{(1)}$, Eq. (3.7), and $-\delta U^{(1)}$, Eq. (3.11)