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Integrability of eccentric, spinning black hole binaries up to second post-Newtonian order
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Integrability of eccentric, spinning black hole binaries up to second post-Newtonian order
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Accurate and efficient modeling of the dynamics of binary black holes (BBHs) is crucial to their detection and parameter estimation through gravitational waves, both with LIGO/Virgo and LISA. General BBH configurations will have misaligned spins and eccentric orbits, eccentricity being particularly relevant at early times. Modeling these systems is both analytically and numerically challenging. Even though the 1.5 post-Newtonian (PN) order is Liouville integrable, numerical work has demonstrated chaos at 2PN order, which impedes the existence of an analytic solution. In this article we revisit integrability at both 1.5PN and 2PN orders. At 1.5PN, we construct four (out of five) action integrals. At 2PN, we show that the system is indeed integrable - but in a perturbative sense - by explicitly constructing five mutually-commuting constants of motion. Because of the KAM theorem, this is consistent with the past numerical demonstration of chaos. Our method extends to higher PN orders, opening the door for a fully analytical solution to the generic eccentric, spinning BBH problem.
Forward citations
Cited by 5 Pith papers
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Non-adiabatic dynamics of eccentric black-hole binaries in post-Newtonian theory
New non-orbit-averaged 2.5PN equations for eccentric non-spinning black-hole binaries derived via energy-momentum mappings, showing Peters 1964 orbit-averaged equations break at first pericenter.
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Analytical Solution of Spinning, Eccentric Binary Black Hole Dynamics at the Second Post-Newtonian Order
An analytical 2PN solution is constructed for the orbital and spin dynamics of eccentric, arbitrarily spinning binary black holes, with spin oscillations retained only at 1.5PN accuracy.
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Unexpected Symmetries of Kerr Black Hole Scattering
The work establishes conservation of several quantities in Kerr black hole scattering and presents evidence that a spinning probe satisfies asymptotic integrability to quartic spin order at all post-Minkowskian orders.
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Closed-form solutions of spinning, eccentric binary black holes at 1.5 post-Newtonian order
Two closed-form solutions for the 1.5PN Hamiltonian of spinning eccentric binary black holes are derived by combining prior methods, implemented in the public BBHpnToolkit package, and verified against numerical integration.
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Action-angle variables of a binary black hole with arbitrary eccentricity, spins, and masses at 1.5 post-Newtonian order
Derives the fifth action for 1.5PN BBH with arbitrary eccentricity, spins, and masses, completing action-angle variables for analytical dynamics solution.
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