Spin-dependent two-body interactions from gravitational self-force computations

TL;DR

This paper analytically computes high-order gravitational self-force corrections for a small mass orbiting a Kerr black hole, enhancing understanding of spin-dependent effects in black hole binaries.

Contribution

It provides the first high-order analytical calculations of spin-dependent self-force corrections and links them to effective-one-body models, improving modeling of spinning black hole binaries.

Findings

Computed 8.5 post-Newtonian order corrections.

Transcribed results into spin-dependent couplings in EOB model.

Compared analytical results with numerical self-force data.

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.