Complete conservative dynamics for inspiralling compact binaries with spins at the fourth post-Newtonian order

Abstract

In this work we complete the spin-dependent conservative dynamics of inspiralling compact binaries at the fourth post-Newtonian order, and in particular the derivation of the next-to-next-to-leading order spin-squared interaction potential. We derive the physical equations of motion of the position and the spin from a direct variation of the action. Further, we derive the quadratic-in-spin Hamiltonians, as well as their expressions in the center-of-mass frame. We construct the conserved integrals of motion, which form the Poincaré algebra. This construction provided a consistency check for the validity of our result, which is crucial in particular in the current absence of another independent derivation of the next-to-next-to-leading order spin-squared interaction. Finally, we provide here the complete gauge-invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to the fourth post-Newtonian order. These high post-Newtonian orders, in particular taking into account the spins of the binary constituents, will enable to gain more accurate information on the constituents from even more sensitive gravitational-wave detections to come.

23 pages, published

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Cited by in corpus (25)

• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Compton Black-Hole Scattering for $s\le 5/2$
• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Gravitational radiation from inspiralling compact objects: Spin effects to fourth Post-Newtonian order
• Classical observables from coherent-spin amplitudes
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• Completing the Fifth PN Precision Frontier via the EFT of Spinning Gravitating Objects
• Spin contributions to the gravitational-waveform modes for spin-aligned binaries at the 3.5PN order
• N${}^3$LO Quadratic-in-Spin Interactions for Generic Compact Binaries
• N${}^3$LO Spin-Orbit Interaction via the EFT of Spinning Gravitating Objects
• Quadratic-in-spin interactions at fifth post-Newtonian order probe new physics
• Renormalizing Love: tidal effects at the third post-Newtonian order
• Post-Newtonian Waveforms from Spinning Scattering Amplitudes
• Large Gauge Effects and the Structure of Amplitudes
• Gravitoelectric dynamical tides at second post-Newtonian order
• Fast inspirals and the treatment of orbital resonances
• From the EFT of Spinning Gravitating Objects to Poincaré and Gauge Invariance at the 4.5PN Precision Frontier
• Charged test-particle scattering and effective one-body metrics with spin
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• Scrambling and Entangling Spinning Particles
• Dynamics for Super-Extremal Kerr Binary Systems at $\mathcal{O}(G^2)$
• The next generation: Impact of high-order analytical information on effective one body waveform models for noncircularized, spin-aligned black hole binaries