Séminaire / Seminar GReCO |
| « Innermost stable circular orbit of compact binaries at the fourth post-Newtonian order » |
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Etienne Ligout |
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In the Newtonian theory of gravity, all circular orbits remain stable under a small perturbation. This is not so in general relativity, where there is an Innermost Stable Circular Orbit (ISCO). However, in the case of the two-body problem, and crucially for a compact binary system, the location of the ISCO cannot be determined exactly. A widely-used approach to circumvent this issue is to resort to the post-Newtonian (PN) expansion. Iterating on the PN order thus provides an approximate expression for the ISCO. In the literature, the ISCO has been determined up to the 3PN order. In the work, we extend this analysis to the next, 4PN order. We use two methods, with equivalent results: dynamical perturbation of the conservative equations of motion in harmonic coordinates, and dynamical perturbation of the conservative Hamiltonian in ADM coordinates. The ISCO is deduced from an invariant stability criterion, extending the 3PN criterion of Blanchet and Iyer (2003). The heart of the derivation of this 4PN criterion is the study of the perturbation of the tail integrals appearing in the dynamics, which are non-local in time. 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. 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 (GSF) 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. |
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lundi 23 juin 2025 - 11:00 Salle des séminaires Évry Schatzman Institut d'Astrophysique de Paris |
| Pages web du séminaire / Seminar's webpage |