Innermost stable circular orbit of arbitrary-mass compact binaries at fourth post-Newtonian order
Phys. Rev. D 112, 064025 – Published 11 September, 2025
DOI: https://doi.org/10.1103/mtv7-lkv8
Abstract
We compute by means of post-Newtonian (PN) methods the innermost stable circular orbit (ISCO) of arbitrary-mass (in particular, comparable-mass) compact binaries. Two methods are used with equivalent results: dynamical perturbation of the conservative equations of motion in harmonic coordinates and dynamical perturbation of the conservative Hamiltonian in Arnowitt-Deser-Misner (ADM) coordinates. The perturbation of the nonlocal tail term at 4PN order in both approaches is carefully investigated. Our final gauge-invariant result for the location of the ISCO at 4PN order is close to the numerical value of the ISCO shift computed by the gravitational self-force approach in the small mass-ratio limit and is also in good agreement with the full numerical-relativity calculation in the case of equal masses. The PN method followed here is considered in standard Taylor-expanded form, without any resummation techniques applied. As a complement, we also compute explicitly the gauge transformation from harmonic coordinates to ADM coordinates up to 4PN order, including the tail contribution therein.
